{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<torch._C.Generator at 0x7f1f1c15ed50>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "import torchvision\n",
    "from torch import nn, optim, autograd\n",
    "from torch.nn import functional as F\n",
    "from torch.distributions.multivariate_normal import MultivariateNormal\n",
    "from torch.autograd import Variable\n",
    "import numpy as np\n",
    "#import input_data\n",
    "from sklearn.utils import shuffle as skshuffle\n",
    "from math import *\n",
    "from backpack import backpack, extend\n",
    "from backpack.extensions import KFAC, DiagHessian, DiagGGNMC\n",
    "from sklearn.metrics import roc_auc_score\n",
    "import scipy\n",
    "from tqdm import tqdm, trange\n",
    "import pytest\n",
    "from DirLPA_utils import * \n",
    "import time\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(123)\n",
    "torch.manual_seed(123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_alpha_from_Normal_old(mu, Sigma):\n",
    "    alpha = []\n",
    "    K = len(Sigma[0])\n",
    "    sum_exp = np.sum(np.exp(-1*np.array(mu)))\n",
    "    for k in range(K):\n",
    "        alpha.append(1/Sigma[k][k]*(1 - 2/K + np.exp(mu[k])/K**2 * sum_exp))\n",
    "        \n",
    "    return(alpha)\n",
    "\n",
    "def get_alpha_from_Normal(mu, Sigma):\n",
    "    K = len(mu)\n",
    "    sum_exp = np.sum(np.exp(-1*np.array(mu)))\n",
    "    Sigma_d = np.diag(Sigma)\n",
    "    alpha = 1/Sigma_d * (1- 2/K + np.exp(mu)/K**2 * sum_exp)    \n",
    "    return(alpha)\n",
    "\n",
    "def get_alpha_from_Normal_batch(mu, Sigma):\n",
    "    mu, Sigma = torch.from_numpy(mu), torch.from_numpy(Sigma)\n",
    "    batch_size, K = mu.size(0), mu.size(-1)\n",
    "    Sigma_d = torch.diagonal(Sigma, dim1=1, dim2=2)\n",
    "    sum_exp = torch.sum(torch.exp(-1*torch.Tensor(mu)), dim=1).view(-1,1)\n",
    "    alpha = 1/Sigma_d * (1 - 2/K + torch.exp(mu)/K**2 * sum_exp)\n",
    "    \n",
    "    assert(alpha.size() == mu.size())\n",
    "    \n",
    "    return(alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "561\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# just copy pasted from this link: http://blog.bogatron.net/blog/2014/02/02/visualizing-dirichlet-distributions/\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.tri as tri\n",
    "import math\n",
    "from functools import reduce\n",
    "from math import gamma\n",
    "from operator import mul\n",
    "from scipy.special import loggamma, gammaln, xlogy\n",
    "\n",
    "corners = np.array([[0, 0], [1, 0], [0.5, 0.75**0.5]])\n",
    "triangle = tri.Triangulation(corners[:, 0], corners[:, 1])\n",
    "\n",
    "refiner = tri.UniformTriRefiner(triangle)\n",
    "trimesh = refiner.refine_triangulation(subdiv=4)\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "plt.figure(figsize=(8, 4))\n",
    "for (i, mesh) in enumerate((triangle, trimesh)):\n",
    "    plt.subplot(1, 2, i+ 1)\n",
    "    plt.triplot(mesh)\n",
    "    plt.axis('off')\n",
    "    plt.axis('equal')\n",
    "\"\"\"\n",
    "\n",
    "midpoints = [(corners[(i + 1) % 3] + corners[(i + 2) % 3]) / 2.0 \\\n",
    "             for i in range(3)]\n",
    "def xy2bc(xy, tol=1.e-3):\n",
    "    '''Converts 2D Cartesian coordinates to barycentric.'''\n",
    "    s = [(corners[i] - midpoints[i]).dot(xy - midpoints[i]) / 0.75 \\\n",
    "         for i in range(3)]\n",
    "    return np.clip(s, tol, 1.0 - tol)\n",
    "\n",
    "def logit_transform(x):\n",
    "    \n",
    "    out = np.log(x/(1-x))\n",
    "    return(out)\n",
    "\n",
    "def beta_function(alpha):\n",
    "    return(np.exp(np.sum([loggamma(a_i) for a_i in alpha]) - loggamma(np.sum(alpha))))    \n",
    "\n",
    "class Dirichlet(object):\n",
    "    def __init__(self, alpha):\n",
    "        self._alpha = np.array(alpha)\n",
    "        self._coef = np.sum(gammaln(alpha)) - gammaln(np.sum(alpha))    \n",
    "        \n",
    "    def pdf(self, x):\n",
    "        '''Returns pdf value for `x`.'''\n",
    "        #x = softmax_transform(x)\n",
    "        return(np.exp(- self._coef+ np.sum((xlogy(self._alpha-1, x.T)).T, 0)))\n",
    "    \n",
    "class Normal3D(object):\n",
    "    \n",
    "    def __init__(self, mu, Sigma):\n",
    "        self.mu = np.array(mu)\n",
    "        self.Sigma = np.linalg.inv(np.array(Sigma))\n",
    "        self.const = 1 / (np.sqrt((2*np.pi)**3 * np.linalg.det(Sigma)))\n",
    "        \n",
    "    def pdf(self, x):\n",
    "        \"\"\"Calculate 3D Gaussian\"\"\"\n",
    "        y = self.const * np.exp(-0.5 * (x - self.mu).T @ self.Sigma @ (x - self.mu))\n",
    "        return(y)\n",
    "    \n",
    "class logitNormal3D(object):\n",
    "    \n",
    "    def __init__(self, mu, Sigma):\n",
    "        self.mu = np.array(mu)\n",
    "        self.Sigma = np.array(Sigma)\n",
    "        self.Sigma_inv = np.linalg.inv(np.array(Sigma))\n",
    "        self.const = 1/ (np.sqrt(np.linalg.det(2 * np.pi * self.Sigma)))\n",
    "        \n",
    "    def pdf(self, x):\n",
    "        part_one = self.const /np.prod(x*(1-x))\n",
    "        logit = logit_transform(x)\n",
    "        part_two = np.exp(-0.5*(logit - self.mu).T @ self.Sigma_inv @ (logit - self.mu))\n",
    "        y = part_one * part_two\n",
    "        return(y)\n",
    "    \n",
    "class softmaxNormal3D(object):\n",
    "    \n",
    "    def __init__(self, mu, Sigma, c):\n",
    "        self.mu = np.array(mu)\n",
    "        self.c = c * np.ones(len(mu))\n",
    "        self.Sigma = np.array(Sigma)\n",
    "        self.Sigma_inv = np.linalg.inv(np.array(Sigma))\n",
    "        self.const = 1/ (np.sqrt(np.linalg.det(2 * np.pi * self.Sigma)))\n",
    "        \n",
    "    def pdf(self, x):\n",
    "        part_one = self.const/ np.prod(1/x)\n",
    "        sm_inv = np.log(x) + self.c\n",
    "        part_two = np.exp(-0.5*(sm_inv - self.mu).T @ self.Sigma_inv @ (sm_inv - self.mu))\n",
    "        y = part_one * part_two\n",
    "        return(y)\n",
    "\n",
    "def draw_pdf_contours(dist, nlevels=200, subdiv=5, **kwargs):\n",
    "\n",
    "    refiner = tri.UniformTriRefiner(triangle)\n",
    "    trimesh = refiner.refine_triangulation(subdiv=subdiv)\n",
    "    pvals = [dist.pdf(xy2bc(xy)) for xy in zip(trimesh.x, trimesh.y)]\n",
    "    xys = [xy2bc(xy) for xy in zip(trimesh.x, trimesh.y)]\n",
    "    #print(len(pvals))\n",
    "    #print(xys)\n",
    "    print(len(xys))\n",
    "\n",
    "    plt.tricontourf(trimesh, pvals, nlevels, **kwargs)\n",
    "    plt.axis('equal')\n",
    "    plt.xlim(0, 1)\n",
    "    plt.ylim(0, 0.75**0.5)\n",
    "    plt.axis('off')\n",
    "    \n",
    "draw_pdf_contours(Dirichlet([5, 5, 5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7kwZvo/Jvz2/F3BIW+gNY58AWOF+/utE9z9DoD/aVXp1cvyyddOMxetUg19VnuapeHfj6+WDqms+enfHo10OFn/1GaTSe/qU66Ckmpaoy8cpGLHQAu5eiUrX06JcF8d2Vsl6ucDp9w9KTfAVJ+YvD67fPXv1Imj7Bl5M/G9YPkZRuxNwSFjoAGMEPFgGAEQQdAIwg6ABgBEEHACMIOgAYQdABwAiCDgBGEHQAMIKgA4ARBB0AjCDoAGAEQQcAIwg6ABhB0AHACIIOAEYQdAAwgqADgBEEHQCMIOgAYARBBwAjCDoAGEHQAcAIgg4ARvw/n9YHQ6IS3UYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import dirichlet, multivariate_normal\n",
    "\n",
    "def softmax_transform(a):\n",
    "    x = np.exp(a)/np.sum(np.exp(a))\n",
    "    return(x)\n",
    "\n",
    "def argmin_norm(sample, positions):\n",
    "    return(np.argmin(np.sum(np.square(sample - positions), axis=1)))\n",
    "\n",
    "def sample_dirichlet_contours(alpha, nlevels=200, subdiv=5, num_samples=10000, **kwargs):\n",
    "\n",
    "    refiner = tri.UniformTriRefiner(triangle)\n",
    "    trimesh = refiner.refine_triangulation(subdiv=subdiv)\n",
    "    xys = np.array([xy2bc(xy) for xy in zip(trimesh.x, trimesh.y)])\n",
    "    dirichlet_samples = dirichlet.rvs(alpha, size=num_samples)\n",
    "    counts = np.zeros(len(xys))\n",
    "    for x in dirichlet_samples:\n",
    "        counts[argmin_norm(x, xys)] += 1\n",
    "    \n",
    "    pvals = counts/num_samples\n",
    "\n",
    "    plt.tricontourf(trimesh, pvals, nlevels, **kwargs)\n",
    "    plt.axis('equal')\n",
    "    plt.xlim(0, 1)\n",
    "    plt.ylim(0, 0.75**0.5)\n",
    "    plt.axis('off')\n",
    "    plt.show()\n",
    "    \n",
    "def sample_Normal_contours(mu, sigma, nlevels=200, subdiv=5, num_samples=10000, **kwargs):\n",
    "\n",
    "    refiner = tri.UniformTriRefiner(triangle)\n",
    "    trimesh = refiner.refine_triangulation(subdiv=subdiv)\n",
    "    xys = np.array([xy2bc(xy) for xy in zip(trimesh.x, trimesh.y)])\n",
    "    gaussian_samples = multivariate_normal.rvs(mean=mu, cov=sigma, size=num_samples)\n",
    "    softmax_gaussian_samples = np.array([softmax_transform(x) for x in gaussian_samples])\n",
    "    counts = np.zeros(len(xys))\n",
    "    for x in softmax_gaussian_samples:\n",
    "        counts[argmin_norm(x, xys)] += 1\n",
    "    \n",
    "    pvals = counts/num_samples\n",
    "\n",
    "    plt.tricontourf(trimesh, pvals, nlevels, **kwargs)\n",
    "    plt.axis('equal')\n",
    "    plt.xlim(0, 1)\n",
    "    plt.ylim(0, 0.75**0.5)\n",
    "    plt.axis('off')\n",
    "    plt.show()\n",
    "    \n",
    "    #return(xys, pvals)\n",
    "    \n",
    "sample_dirichlet_contours(np.array([5, 5, 5]))\n",
    "sample_Normal_contours(np.array([-1, 2, -1]), 0.1*np.eye(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# check out the KL divergence for one example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import loggamma, xlogy, gammaln\n",
    "\n",
    "\n",
    "def logit_transform(x):\n",
    "    return(np.log(x/(1-x)))\n",
    "\n",
    "def dirichlet_pdf(x, alpha):\n",
    "    alpha = np.array(alpha)\n",
    "    lnB = np.sum(gammaln(alpha)) - gammaln(np.sum(alpha))    \n",
    "    return(np.exp(- lnB + np.sum((xlogy(alpha-1, x.T)).T, 0)))\n",
    "    \n",
    "def logitNormal3D_pdf(x, mu, Sigma):\n",
    "    \n",
    "    mu = np.array(mu)\n",
    "    Sigma = np.array(Sigma)\n",
    "    Sigma_inv = np.linalg.inv(np.array(Sigma))\n",
    "    const = 1/(np.sqrt(np.linalg.det(2 * np.pi * Sigma)))\n",
    "\n",
    "    part_one = const / np.prod(x*(1-x))\n",
    "    logit = logit_transform(x)\n",
    "    part_two = np.exp(-0.5*(logit - mu).T @ Sigma_inv @ (logit - mu))\n",
    "    y = part_one * part_two\n",
    "    return(y)\n",
    "\n",
    "def softmax_normal_pdf(x, mu, Sigma, c):\n",
    "    mu = np.array(mu)\n",
    "    Sigma = np.array(Sigma)\n",
    "    Sigma_inv = np.linalg.inv(np.array(Sigma))\n",
    "    const = 1/(np.sqrt(np.linalg.det(2 * np.pi * Sigma)))\n",
    "    \n",
    "    part_one = const/ np.prod(1/x)\n",
    "    sm_inv = np.log(x) + c\n",
    "    part_two = np.exp(-0.5*(sm_inv - mu).T @ Sigma_inv @ (sm_inv - mu))\n",
    "    y = part_one * part_two\n",
    "    return(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha1:  [6.66666667 6.66666667 6.66666667]\n",
      "alpha2:  [4.90789709 0.56108745 0.56108745]\n",
      "alpha3:  [2.78728188 1.39364094 0.91101647]\n",
      "alpha4:  [23.00125657  0.4860686   0.74851083]\n",
      "Dirichlet x1, a1:  15.998067072830981\n",
      "Dirichlet x1, a2:  0.08609075690213953\n",
      "Dirichlet x2, a1:  0.002707938331158549\n",
      "Dirichlet x2, a2:  7.581916853300082\n",
      "logitNormal x1, m1, S1:  0.13567391195402193\n",
      "logitNormal x1, m2, S2:  0.14011904024999516\n",
      "logitNormal x2, m1, S1:  1.1223088716939438e-22\n",
      "logitNormal x2, m2, S2:  9.679333903157055\n",
      "softmaxNormal x1, m1, S1:  0.06427139733022627\n",
      "softmaxNormal x1, m2, S2:  0.00011538467163493116\n",
      "softmaxNormal x2, m1, S1:  3.3614598920171183e-11\n",
      "softmaxNormal x2, m2, S2:  0.00021937517873910986\n"
     ]
    }
   ],
   "source": [
    "### test cases:\n",
    "\n",
    "mu1 = np.array([0,0,0])\n",
    "Sigma1 = 0.1*np.eye(3)\n",
    "t0 = time.process_time()\n",
    "alpha1 = get_alpha_from_Normal(mu1, Sigma1)\n",
    "t1 = time.process_time()\n",
    "Dirichlet_1_time = t1 - t0\n",
    "print(\"alpha1: \", alpha1)\n",
    "\n",
    "mu2 = np.array([2,-1,-1])\n",
    "Sigma2 = 1*np.eye(3)\n",
    "t0 = time.process_time()\n",
    "alpha2 = get_alpha_from_Normal(mu2, Sigma2)\n",
    "t1 = time.process_time()\n",
    "Dirichlet_2_time = t1 - t0\n",
    "print(\"alpha2: \", alpha2)\n",
    "\n",
    "mu3 = np.array([1,1,-2])\n",
    "Sigma3 = np.array([[1,0, 0.5],\n",
    "                   [0,2, 0.3],\n",
    "                   [0.5, 0.3, 0.5]])\n",
    "t0 = time.process_time()\n",
    "alpha3 = get_alpha_from_Normal(mu3, Sigma3)\n",
    "t1 = time.process_time()\n",
    "Dirichlet_3_time = t1 - t0\n",
    "print(\"alpha3: \", alpha3)\n",
    "\n",
    "mu4 = np.array([3,-2,-1])\n",
    "Sigma4 = 1*np.eye(3)\n",
    "t0 = time.process_time()\n",
    "alpha4 = get_alpha_from_Normal(mu4, Sigma4)\n",
    "t1 = time.process_time()\n",
    "Dirichlet_4_time = t1 - t0\n",
    "print(\"alpha4: \", alpha4)\n",
    "\n",
    "x1 = np.array([1/3]*3)\n",
    "#x2 = np.array([0.999, 0.0005, 0.0005])\n",
    "x2 = np.array([0.8, 0.1, 0.1])\n",
    "\n",
    "print(\"Dirichlet x1, a1: \", dirichlet_pdf(x1, alpha1))\n",
    "print(\"Dirichlet x1, a2: \", dirichlet_pdf(x1, alpha2))\n",
    "print(\"Dirichlet x2, a1: \", dirichlet_pdf(x2, alpha1))\n",
    "print(\"Dirichlet x2, a2: \", dirichlet_pdf(x2, alpha2))\n",
    "\n",
    "print(\"logitNormal x1, m1, S1: \", logitNormal3D_pdf(x1, mu1, Sigma1))\n",
    "print(\"logitNormal x1, m2, S2: \", logitNormal3D_pdf(x1, mu2, Sigma2))\n",
    "print(\"logitNormal x2, m1, S1: \", logitNormal3D_pdf(x2, mu1, Sigma1))\n",
    "print(\"logitNormal x2, m2, S2: \", logitNormal3D_pdf(x2, mu2, Sigma2))\n",
    "\n",
    "print(\"softmaxNormal x1, m1, S1: \", softmax_normal_pdf(x1, mu1, Sigma1, c=1))\n",
    "print(\"softmaxNormal x1, m2, S2: \", softmax_normal_pdf(x1, mu2, Sigma2, c=1))\n",
    "print(\"softmaxNormal x2, m1, S1: \", softmax_normal_pdf(x2, mu1, Sigma1, c=1))\n",
    "print(\"softmaxNormal x2, m2, S2: \", softmax_normal_pdf(x2, mu2, Sigma2, c=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1512x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(nrows=1, ncols=3, sharex=False, figsize=(21, 5))\n",
    "\n",
    "mu = mu1\n",
    "Sigma = Sigma1\n",
    "alpha = alpha1\n",
    "num_samples = 25000\n",
    "subdiv=5\n",
    "nlevels = 200\n",
    "#VALUES\n",
    "#softmax(samples)\n",
    "gaussian_samples = multivariate_normal.rvs(mean=mu, cov=Sigma, size=num_samples)\n",
    "softmax_gaussian_samples = np.array([softmax_transform(x) for x in gaussian_samples])\n",
    "#dirichlet_samples\n",
    "dirichlet_samples = dirichlet.rvs(alpha, size=num_samples)\n",
    "\n",
    "#PLOTS\n",
    "refiner = tri.UniformTriRefiner(triangle)\n",
    "trimesh = refiner.refine_triangulation(subdiv=subdiv)\n",
    "xys = np.array([xy2bc(xy) for xy in zip(trimesh.x, trimesh.y)])\n",
    "#plot softmax(Gaussian) samples\n",
    "counts_n = np.zeros(len(xys))\n",
    "for x in softmax_gaussian_samples:\n",
    "    counts_n[argmin_norm(x, xys)] += 1\n",
    "\n",
    "pvals_n = counts_n/num_samples\n",
    "\n",
    "cs = axs[0].tricontourf(trimesh, pvals_n, nlevels)\n",
    "for c in cs.collections:\n",
    "    c.set_rasterized(True)\n",
    "axs[0].axis('equal')\n",
    "axs[0].set_xlim(0, 1)\n",
    "axs[0].set_ylim(0, 0.75**0.5)\n",
    "axs[0].axis('off')\n",
    "axs[0].set_title(\"Softmax of Gaussian samples\")\n",
    "\n",
    "#plot Dirichlet McKay pdf\n",
    "dist_McKay = Dirichlet(alpha)\n",
    "pvals_McKay = [dist_McKay.pdf(xy2bc(xy)) for xy in zip(trimesh.x, trimesh.y)]\n",
    "\n",
    "cs = axs[1].tricontourf(trimesh, pvals_McKay, nlevels)\n",
    "for c in cs.collections:\n",
    "    c.set_rasterized(True)\n",
    "axs[1].axis('equal')\n",
    "axs[1].set_xlim(0, 1)\n",
    "axs[1].set_ylim(0, 0.75**0.5)\n",
    "axs[1].axis('off')\n",
    "axs[1].set_title(\"Dirichlet pdf\")\n",
    "\n",
    "#plot logitnormal\n",
    "\n",
    "dist_logitNormal = logitNormal3D(mu, Sigma)\n",
    "pvals_logitNormal = [dist_logitNormal.pdf(xy2bc(xy)) for xy in zip(trimesh.x, trimesh.y)]\n",
    "\n",
    "cs = axs[2].tricontourf(trimesh, pvals_logitNormal, nlevels)\n",
    "for c in cs.collections:\n",
    "    c.set_rasterized(True)\n",
    "axs[2].axis('equal')\n",
    "axs[2].set_xlim(0, 1)\n",
    "axs[2].set_ylim(0, 0.75**0.5)\n",
    "axs[2].axis('off')\n",
    "axs[2].set_title(\"logit-Normal pdf\")\n",
    "\n",
    "plt.savefig('logitNormal_comparison_v1.pdf')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1512x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(nrows=1, ncols=3, sharex=False, figsize=(21, 5))\n",
    "\n",
    "mu = mu2\n",
    "Sigma = Sigma2\n",
    "alpha = alpha2\n",
    "num_samples = 25000\n",
    "subdiv=5\n",
    "nlevels = 200\n",
    "#VALUES\n",
    "#softmax(samples)\n",
    "gaussian_samples = multivariate_normal.rvs(mean=mu, cov=Sigma, size=num_samples)\n",
    "softmax_gaussian_samples = np.array([softmax_transform(x) for x in gaussian_samples])\n",
    "#dirichlet_samples\n",
    "dirichlet_samples = dirichlet.rvs(alpha, size=num_samples)\n",
    "\n",
    "#PLOTS\n",
    "refiner = tri.UniformTriRefiner(triangle)\n",
    "trimesh = refiner.refine_triangulation(subdiv=subdiv)\n",
    "xys = np.array([xy2bc(xy) for xy in zip(trimesh.x, trimesh.y)])\n",
    "#plot softmax(Gaussian) samples\n",
    "counts_n = np.zeros(len(xys))\n",
    "for x in softmax_gaussian_samples:\n",
    "    counts_n[argmin_norm(x, xys)] += 1\n",
    "\n",
    "pvals_n = counts_n/num_samples\n",
    "\n",
    "cs = axs[0].tricontourf(trimesh, pvals_n, nlevels)\n",
    "for c in cs.collections:\n",
    "    c.set_rasterized(True)\n",
    "axs[0].axis('equal')\n",
    "axs[0].set_xlim(0, 1)\n",
    "axs[0].set_ylim(0, 0.75**0.5)\n",
    "axs[0].axis('off')\n",
    "axs[0].set_title(\"Softmax of Gaussian samples\")\n",
    "\n",
    "#plot Dirichlet McKay pdf\n",
    "dist_McKay = Dirichlet(alpha)\n",
    "pvals_McKay = [dist_McKay.pdf(xy2bc(xy)) for xy in zip(trimesh.x, trimesh.y)]\n",
    "\n",
    "cs = axs[1].tricontourf(trimesh, pvals_McKay, nlevels)\n",
    "for c in cs.collections:\n",
    "    c.set_rasterized(True)\n",
    "axs[1].axis('equal')\n",
    "axs[1].set_xlim(0, 1)\n",
    "axs[1].set_ylim(0, 0.75**0.5)\n",
    "axs[1].axis('off')\n",
    "axs[1].set_title(\"Dirichlet pdf\")\n",
    "\n",
    "#plot logitnormal\n",
    "\n",
    "dist_logitNormal = logitNormal3D(mu, Sigma)\n",
    "pvals_logitNormal = [dist_logitNormal.pdf(xy2bc(xy)) for xy in zip(trimesh.x, trimesh.y)]\n",
    "\n",
    "cs = axs[2].tricontourf(trimesh, pvals_logitNormal, nlevels)\n",
    "for c in cs.collections:\n",
    "    c.set_rasterized(True)\n",
    "axs[2].axis('equal')\n",
    "axs[2].set_xlim(0, 1)\n",
    "axs[2].set_ylim(0, 0.75**0.5)\n",
    "axs[2].axis('off')\n",
    "axs[2].set_title(\"logit-Normal pdf\")\n",
    "\n",
    "plt.savefig('logitNormal_comparison_v2.pdf')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1512x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(nrows=1, ncols=3, sharex=False, figsize=(21, 5))\n",
    "\n",
    "mu = mu3\n",
    "Sigma = Sigma3\n",
    "alpha = alpha3\n",
    "num_samples = 25000\n",
    "subdiv=5\n",
    "nlevels = 200\n",
    "#VALUES\n",
    "#softmax(samples)\n",
    "gaussian_samples = multivariate_normal.rvs(mean=mu, cov=Sigma, size=num_samples)\n",
    "softmax_gaussian_samples = np.array([softmax_transform(x) for x in gaussian_samples])\n",
    "#dirichlet_samples\n",
    "dirichlet_samples = dirichlet.rvs(alpha, size=num_samples)\n",
    "\n",
    "#PLOTS\n",
    "refiner = tri.UniformTriRefiner(triangle)\n",
    "trimesh = refiner.refine_triangulation(subdiv=subdiv)\n",
    "xys = np.array([xy2bc(xy) for xy in zip(trimesh.x, trimesh.y)])\n",
    "#plot softmax(Gaussian) samples\n",
    "counts_n = np.zeros(len(xys))\n",
    "for x in softmax_gaussian_samples:\n",
    "    counts_n[argmin_norm(x, xys)] += 1\n",
    "\n",
    "pvals_n = counts_n/num_samples\n",
    "\n",
    "cs = axs[0].tricontourf(trimesh, pvals_n, nlevels)\n",
    "for c in cs.collections:\n",
    "    c.set_rasterized(True)\n",
    "axs[0].axis('equal')\n",
    "axs[0].set_xlim(0, 1)\n",
    "axs[0].set_ylim(0, 0.75**0.5)\n",
    "axs[0].axis('off')\n",
    "axs[0].set_title(\"Softmax of Gaussian samples\")\n",
    "\n",
    "#plot Dirichlet McKay pdf\n",
    "dist_McKay = Dirichlet(alpha)\n",
    "pvals_McKay = [dist_McKay.pdf(xy2bc(xy)) for xy in zip(trimesh.x, trimesh.y)]\n",
    "\n",
    "cs = axs[1].tricontourf(trimesh, pvals_McKay, nlevels)\n",
    "for c in cs.collections:\n",
    "    c.set_rasterized(True)\n",
    "axs[1].axis('equal')\n",
    "axs[1].set_xlim(0, 1)\n",
    "axs[1].set_ylim(0, 0.75**0.5)\n",
    "axs[1].axis('off')\n",
    "axs[1].set_title(\"Dirichlet pdf\")\n",
    "\n",
    "#plot logitnormal\n",
    "\n",
    "dist_logitNormal = logitNormal3D(mu, Sigma)\n",
    "pvals_logitNormal = [dist_logitNormal.pdf(xy2bc(xy)) for xy in zip(trimesh.x, trimesh.y)]\n",
    "\n",
    "cs = axs[2].tricontourf(trimesh, pvals_logitNormal, nlevels)\n",
    "for c in cs.collections:\n",
    "    c.set_rasterized(True)\n",
    "axs[2].axis('equal')\n",
    "axs[2].set_xlim(0, 1)\n",
    "axs[2].set_ylim(0, 0.75**0.5)\n",
    "axs[2].axis('off')\n",
    "axs[2].set_title(\"logit-Normal pdf\")\n",
    "\n",
    "plt.savefig('logitNormal_comparison_v3.pdf')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "561\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#sample_dirichlet_contours(alpha1)\n",
    "sample_Normal_contours(mu1, Sigma1)\n",
    "draw_pdf_contours(logitNormal3D(mu1, Sigma1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "561\n"
     ]
    },
    {
     "data": {
      "image/png": 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VPYdvo5dZf7oFSGeAhtMCKcACKfkQFHTyrVwthJbbaz3ny66WS1FLP3fmJTPXg+fmeNEpVomKECYR72IWcnFxBwBEQE2QTDCmUMU9pQBVgc+VCF8ZCQFaJ/kqV1zAtZkHpi6UYQGi6p/HANMi6E2BtCwqHcQLpONYC6R06eQcFPQn5N7u3K82bvyGQugsaul88FBaDOZxR95k5geDHRTIOXnoFbFT9F3CSz9WEe9jQgyKPpwK4qARSQOGFJHMXfv70HmtNBjSO4CXLOoocYsLd4ldipi7eovP79IJtG1lXIteSm/6YgQp6NLJGSjo5Nu45M79xpVC6LmopQp4FvU2N+9Qi5VLMe/7hEM/oouKQ0w4dCP6kBDEcFgRcwA4xIRRfR8GjTiO01emuHkdzBOW4FFMyc6rS1/k6doLkgLdWFZOknn0Mi4KpNrMmw74rxuwjZGcQkF/MjbbpgicFkLbqCXA3fmV3HwWsxwU0iniIaHrFId+RN8lvHYjXrvBRT0kdEFxCCPOcdQOowYcNaIPCXHsIWIYRv8MoxgSAEPMxVM3zjZ6G2Wbp4fRT0RhBDQPOIopL15dul3aNsZzBVK2MZIVKOhPxL2jlurObxgRii74akKCPH/L5M7TrB3xtBBqnRdAQxbz4sxfuoTXfkAfEl7jiF/dgEMcL4o5ALzGAUftcEwd/kFft0fxwqqIf40SyqSJAVBBbWtv8nRNkrNyuGMfbyyQtgVRYBMunaK+PSjo5Mu52qZYHnNpROilQmgTtbSiXnrN0VntZun7hD9eBnRB8doPeMlC/qs74hAS/uze8XJF0AHgXTv8R14AAF1QBDG8h+nrYzlfN3VxVrUct0x5uiQ/GUly5+4u/YYC6XIEqRkXwiCrUNCfhE24c2C9TTFvv1YInS1Q0U0uvc3N0fvgnzYzP8SE127AH/3grjyMeI0D/opH/Nm9I2K9IFoYNOIljIgwBFG8JXfpXfDmxSB+W01gmmpmrhryHDBS54KB+T6LAungYr9WIJVRp18zY1qdYpdtjGQJBZ18KR9y58DMnfuISdQ8uVxmhdBW1Nvopc+5eW+QqOjamKUR89c44M8s5C9hxN/xDUEUvVwQ9BA9Rsn04g69CDuQxdwGvBkwaHHrBssxi2gW8uSfQ5J3u3iEJLVAalF8ioGObYzk41DQn4BNu/Mb2hQtLgqhMUfMdWSoz89ivSL0CbH33LzPmfkf/YC/uiN+dZOQ/wpH/NW94VVG9DLiNQyrH+FoHdQEg3UIoohQ/KMHAEAn0/AihfesD2OE9gljElgPaIqQzlzUU46HEiDdvEBqn2xjpEsnLRT0nXPXZeXKtkvuXEoP+uTO2zZFjXkmxYiTQqjFJjfPQ/pDr+g6xUs/4rUbZ5n5n907fsUBf8U3/BXf8CoDghj+DO8IUBxWXPrRIhQB/9EX9Db6iSIlRDH8kx26QjBqQOoC7CW785eEBAGSQjW4mI+S3TlgycVckk8LIOnUpSPgdJ4XYNWl37tASrYBBZ18D7csK3fGnSPIrE2xOPSU1wNto5ZSDC1RS+wUL4eh5uY1Zune8X+6N/wd3/ASBvwKxyrkr2HAQRJe5Tj7CEfr8IqAo0XkORIR1M+PHtH8iVEjxhgwdsFHlmrA2I8+VcCosF5gybJ4e3ZuI6qwSy8IeZ51Xc6b/gGXPjvudOlPCwV9x2zFnfuNtWXlbhtEVNoUZ7l5LoRa510tiOpRS5dqbu6tiUf8GY/4FQe8ZiH/O/6LF8kiHgYEKP4M74gw9OLFzwSPWRIE/9EXHGLCm/YIQXGQEf+DPzBEHz06WMCvbnLpRdi1F4xJgK6Ies7Oc2+6qE/Dm3K2LsnFfNbGGNLDuHSK+v2hoJOv59wgImDuzttBRLHEL+7Oy/qgxaHXEaGtM6+FUJ1HLf2iCNq940U8avk7/ou/w9uJkL/KgF5SFnXFYAFJRgwWfbIuiLt5BLypC2SCjx4doxdNf3UDFDJFMClAe4XmWRpNpwKpJP+10bYx6giE5OKPkAcbfWBKgHsPNiL3h4K+Ux7dnc+mxm0c+rSMXF5xKC9U0TUtin3wEaCHOOKPOOAljPire3N3Ht7wK7zjIGMtiLqgj+hF8SouhK+ieLOAmIueCZ5pDxaB4Nn6r3DE0EUkBCQIRgs4aMQxjz6NURGiQkMAovlAqfp3al+c5k0HNK649LUpAYCZSwfAwUaEgk6+mC9w56WzpV4EdS3Qelm48xDM52jpXNR94NCIl+AdLK8yemYuWsW8uPJXSejFsjtvP4yiF0NvijeLiDC85ZGix+DF0nft8R4GvIcOhzDiEDrP7/sBowYMY4RE31cbLX+mbLLz59KInJuXQu/Cpa9NCUCXTlbgikU7ZFPuvNxeuvNFZ0sr4Bqb9sTFpWbnjTsP0d1wl2dMPOTLX/GIX+GIlzDgJQx4lXIZm78Jr6J4FcPfIeBVpovftnx/WpwE/LXKa78E/zXgUwkkBJjvT+dtlIgK5CXwyq+LEiHVz9a49PZ4+MkO57P09t+gXdnoyr/Td8GVje4HBX1nbOXLdNLZAszd+ZW+8+JkNa4Lu8U8xD/6IhVdTOhjqhNuvYTcshg9Zvk7/Ju7WXLfuYz4FYqYC14lIEBOLi7ugldR/Aqpivkh967/Gd7xKj5A6Vccskv3feljQhcTQvT9RBbzWgNohLz8Aik1A+vyLxjxWRyLkFsX/YQYF79+iksP2/hKb+X/w2eDkQv5NGszKp5153XOltvdua/F2QwgKtl5NHfn0RDK/ObdPDvvQsJLdtCv+RKg2WWXvNyqkPcXvE0QBaBIMAySMFjEq4w4Wodf4d27XSB4kQF/5Im8DiFhCAldXkQjdb6UHfL+++fKfeljjl26afSoJEEo6482c7yIWY5fOp+4q52JsVCzdHCOlydjG6dz8iVswhU164Rec+cIixkVm1GhM/fainpTFC1958Wd93GaCvcluDt/laG2KP4Z3psiqCJC8IKIX9LjRbqzl1/S4y/pECHopRRQPZM/iJ84XmXAr3jES/DZG1+70fepxC5RIUFr3DL7PCex0g0uXeT0xNm69Hj/r/Ym/n98MujQyac4686Xj1m6876r7ryueh/W3flq1NI1o0K7aQm5GDRn51NnS+vOX+U462bpBXiRgF4iXqTHLfRIeIViEMUrRgzW4VWOOIaIdxvwP6o1S39LvRdIuxFDLo6mXmFjdumdjxxtT1aS3KWHcZrjRUaZiqNdWHfpoy+IN+t4QXHkoEt/Iu5/Gidfwlbc0Ko7B6o79wfJzJ1rF9yNBtQLpOkEWbYqCgDkRZ5DXgs0FyFD7laJ0Ny1MolXL2P+Ox2qgMV+XqA8tjy/vJ5fT7mP3cUziNXZGGPeTxEv4iIaTADk16mfKV9qpl4uJZJqT44xnLj0emyZpT8t2/hXJw/FLdl5pTjJIuLLVkW0Il66OvI2wanIC2DBICGLeRHx4ELa5T7yS9PhAkD8gJDfSoT5ikawuh9lv2Lw1koJBgu2EOypfbF+zurKc7FYpuNj+TgCmIb/r+5Q/neR+b/LT3a8kJ+Fgr4DNueClgOJ2o6MZTE0L2BhoXXoHre0Lr2IPIK5PuVtkl1uccQA0GUxbx10oQwUKigMg11e4KK9v5wIlq/Tvl95/7I/Ia9sVPc5f47l55tOWDL9KqkjRqdBWrMWxhh9et0QTlsYN8Lm/v/cMRT0B+envyyX3PnJQCJgil/aYl6OWwAvhiJMI0OLK8fCnVsjgpDs0LOYFxcc8gIUUezi/OYtgyXoijhP949Z9G97vfK+QSYxj62wB/OoRbweUD7b1MUz/TqZpgqWugyfv9Aidlm69EVxdM2l/zQU9Z+Bgk4+zzWRyKMbkTtaEOdxS21V7GTu0pu+7CrsJXcOBgRAciYdc+xS3HBfhfT8KMk1d33NpQO4KPyz1xefD6bk+gAQgz9X8v4jTDl6m6HPT2b5OC1y9Bq7dGFy6WUa4hvZopMnvw8F/YG5uzsv2xatijVuadx5dZPL3vM2K8+92Zajh7Yg2opdKYgCTeQCm6KOG925wjBAq0tfinrrzgdMJ4i1E0JLef+yPzFoXky67PcUv0zRSr5eiqJlYFUZOZpFfRohivlxrSdOWW1h3EKWTpf+/VDQyee4xZ2XKKAphs66W9qRocsi6FLoSuTSTQXRECYxB0qO7iLaLhm3RoJhMKuifokBmoXdkC7GM1MXcNmPAJv2r3HpFqYpANZOXCfHoyttnYIptsrF0U+6dLI/+K//oGzB7ay5cwDzYmj5m/PfmgMvKHHLrc0nqqcPVJtvG6zDYD617bERW5/rfCHqjUsvl/l2y4/355f50n2JuuCzMJ7b19/oqCmxy3JbPY7t8SzHO7TbmKU/ExxY9IDc40tx68/z2fqhwFyMipZIM1gmrIjdYlMbh5sCyIswa/lb5yCPGDXiXTtEHHzxZ+19/hUMeLPeF69QwaskJFhezMIwwNAjzfrS14R8MMGbRQzmw/3frPeL9nizDv+kA961q/ui8MUu2v21lZPRyecvEdOSVuADfMh/DNOqRct1Ru3y/yocaLQvKOjk46yMCp2xnBEQmA0qqrMIZj7izFvMBEnzsm/q6veuHTr1NT979RkSB4u+2hAUCMArhjofSy86E/YlrZAPFvCWVzF6sx7/0Zfqzt+s96l0rce7dnjXblroQgPSmpg318tJa03EZwXSds3R9riW6yV20XWRXhs9+tNwzvTvg4L+YGzqJ+vqQCKZ5m1p8nO/bzF3y/LpTWZ8DlG3r6YCNcmi7su+HTXiYAGjRqQwYtCIt9BVlx5MAQUGcTFPEESbpgN4s/ko0iFHOK0jH6zDm3V4swOOWcjftK8njffU4d/U46gRY94vwE8+UyQk+XNcofSnZzxXn+Z2kTwxl4lMD4u56KCLCbvKfel+Qt5CUf8eKOjkKjM3vnDnp90tK+4cWF3IAkXc1wQ8b591H6oA2UWbCmCoYl5c+jF16ERnLr2XVBd3VgnQ4Jl6WX6uCHsvCW+L02Ur5GV90TfroRaqSy/ufMyP1XxSKe687B8s7/clTT1zUvOWTYEFm2XkFgIEOhVGx7G69BqnlMUvciyzdOmMXfYDBf2BeBh3XihtdYtCaO1Db4SrxgoLWmETy5GwAshvoypIOUc/akSnik4jQurzEPy+rhUKuDs/WsRrGKAa8CpHF3QY3mx9ki4X9Ig3O+BNexwt4t16HK3zmEX7E3deLoq8fyrzQm4ZX9RELefjlpX7cvwiI/z4Ws7RZzULoUt/Mijo5CJLdz6771yL3GrcgipCl6g96Mv9UEwJt7k7VxXE6HHGcewQYDgGRacdghjei1PHAYALs4rgKB0UASoDjhLxKsPFfVIEHHO3zJSdS3XmpRD6rh2O9RIxpIjj2MFsLuTes3nDcQjTLxIg/2JZ5uilMApMLr0sUadz4ZYQqkvPG+6apZOvh4L+IGzFnZ8UQ/Pti0XS5cyL5x6mBjFxJ97eUcbiKGDJF1ounS5mgjEFHzWqETFp7f0u0QsAJHjx8l16vIQBaoL/yAv+DO91ndBLKMKJkNfcPIv5u3Y4pg5vY4djihg0YtCAMYXa6WIqMJ3cuaTps7Xxkt9vuDDgdcYsR2+PaZxPqTvb3sQs94pd6NK/Fgr6A7AVMT/LjYJ98SUUc2FrBC/k91DJPxKSAFGgY8AoBqDzjPoM/0qPP6Iv5BzF8JIXowiieFcX87WJvAplwNBbjlgG9cjlPXmu7jFLh7fU45+xx79Dj7exxzFFvA8dUgrQJNAhAOrOWpLPdS5JEMbp8y6PwU2zDcjcya/eHyPAnHz3UNDJbbRxy7n8/NooRTNIOhWeVshaN14uFvO21Lj05O9XJKrtJkkakLpQc/VDSDiqF0t94YsO/+gBL2HE/8f16XYH9V8fCaH2mBdHPpoXYktmvhTzYYzQJEhDhGkAhgAkmbnzS8eg3DeJvB9DSaWgcIEL7YvTwb9/7EKX/nVQ0DfO5t05ljn7me9l6X4BXIyiQVQmwUYTQxRxS643Etylq3gRUAJcGIPC4KJuZ0TpGKIvHK0RXVBfXSh0PuhIFF2YCqbdiqiPVcx94NJgAUftcpukxysKwTFFJA0nYp7GAB0DLLmQozjzYXIwczMBAAAOGElEQVTnkqaT1exy7V/+ll9GQU5WMtpSYbRAUf8aKOjkLFWosztfzc+X64auYFecuwuYeaGvzdFbgZcseqO4qRQAg2RzGaAr4qcmCGIYuhH/wtDHhEPo8rqjaZpvJStnWZSiZcztJeUXwJid+KihFj4VXpQtefkxxywpBegQYBpgWcCRmsiliHhaxC05P/djcyVHD8GLpcteyBKzlCLoivjX3Dy7dLYvPj4U9A2zZXd+0uHS3i7isdKyePI6KwXQKnJ5YI2EqSe9utkI2BD8RAAFYoBi6k9XFYRg6GLCoKH2pL8HRR/SbEGMdprb8hdAHX06aqjzsZTBQoO6Ix9SRMqF2TFFb6NMAeMQPRoaAywJJEctIWHmyGeftxRIm0Jpe5xWz1qFKEAx4bPWxSZ2WfSjbw269N+Hgk4us3Tn5/LzQrn/ShwgCpgakIWyOvGSl5fIoYldIEX8BGGALxDhI24ANY+e1TBiEvSUAo5i6LuEUb0bpm+WhWsXxyjbCqXQWsQ85YFCADDkrpUx+QLQ1vSaa3bmUAGGMBVAFTVqqbFKI/ChiV3a49Rm5aI4L+wxrBc+1/rRyS6hoG+Ue7vzT8+VndTn5jbz6yJ1EFBFDWIlQ7eclUsV8jBOQq99Frvcul1OJ6YCS34/Sn3QAtCbi2oIkJin2o2KlIKvQRoVQxbtMpd6DNP86rEJrlNui/SPNRVd/XaOVBoR933yHbXURCylm2VAjVpKdl4zdG1uqyEs2hlL9CIrhVBRBZJ9SS5+79iFLv33oKBvkHuL+YdRuzgRs6h61m3iXRomQMoLPowu5lXIxdPgAJu5fN+W/5o3Zljyk4CVsTRJ3PWX9To7g4m5uAeDRBd3YJqbvDRv13U/F8zmYMl3t7Mm+nvms40JMOYTU2qc+NAIepOZhwGQ0UU8DPnvaNP9Y+5oMUDGqbvF18jIZ7G1+GQp+peimg1CUf88FHRywm+vZGNV+SAWYGaz+Usk+fJrxaWHMd8OAkmGPDtJjkEWol4EPPlfUfgSdrlbxtQH2UAAG13YEc3FfTRoyJkO4MvBATmnXxe9OjuiLW7D52SxlCfaSpOQ12H9o9RC7kk3S4lZVsTcc3ar7nwSdvNfN8nyL5t8XK3ctyLu5/LyC50u93bp5PNQ0DfGI7jz1SH/qvMul5SArssRTM7hkyudBcxcugUXMQvIYm4IJvm84KJuuXXRnXkj3ln0VH3JNhulvodF8bU7g0ziDkwOHvDJroCL6z6UjkhpxV1LC6ZMc7Lo1LkCk3mMkly423764tJDctGe4pdy3RBSFnEFZNDJnbe0cctnhXgD/egtdOmfg4JOvo4i4ifbDSJT7CLq20yAMGpems47QLyz3GcVVEhOclzUVTEtSVdEPU4DjzCiTvI1LefmUwXUOWSCTfPLuJGf5o5Zc+nqQ+prGmPN9dxHXyOWxUjPctuz8+bSiHpIQBisydQtjxy1qUiaDGHMuX925yVukUsdK2fE/WROF7IbKOgbYgvu/Oa45ZbHZScpZjV2kWRZgD1Lt9JnPVoWb9/mAjwXdUlSxVxrbp6jlyLwVcinv/Pl7cp137c6i6HU/6x8jvyQooHlpJTvWwp4FfIypL/pYoE13SwzN966dM/Jw2iQsXHpTXZ+Erc0x/siN04BsIXYhS7941DQyXk+s/7kOVFpXLoguKAmA6IgjArNsh3UfEFkIC8HZzlWEWi0LOBSBVwjgCzwJ0K+FHigarbN5hS/4VAsWwmBudC3Ar4U9lbIG9ddHLo78MaNJxfy+rhSGJ1l5zp1twCnWfkt4o6FcG8sdiEfR+zGf3jyvWzBnQMrDr0R9dmi0MB8YQvA2xXL6NEYPH6pq9IHWOfD/60LsN4fZzHU6WAt+sr2FgXW+XqjLtQC7VBzcQvZoUeZC7hMIm6CmcADp9dnQn7JBzb/MrM+cVu5XgqiRbhnjt0WDj2LehOxhHEqfIZkNTd3YVd35EOCjPn6qJ6fq9/GOPptM2AYaodLXV80i7epP2/mwhdifm+HXqBLvx0K+gbYipgDtwm6bw6zof++WlER7+jiXoafXxP1vF6mdgLrfQ71Iura5f5vacS8K9k4phWPSl7eCHxx7cAk3s0qcDc585Pjk8UZaMS60Ij1FMXYdL0K/dyRt1PllvbEMCqglk8CU25+UcyLaI/Jr6u/RhXm/Jianz+IoAMU9Vth5EI+RtL5aFFr+sXVAORul/K4vARaiQQEcFFXQIYE62PufpHa2WJRPIIxQyidJUFgyaBN3DKt5pPbFIPNBD4UgS9vjLmwf1bQS1F0LXppBbzO9dUK9ixusTrys4wIDSViSS7YtQAKP141Nz8n5qXbJYv57N+p5cogpC2JObkdOvQ7syV3Xji3SlE7/H8Zu9T7W5deopczTt1inAYkNWuOWgzVrQOYFpQuy9a1cQym7UAj8lFmgm0LQV/L0q8elyKQC0FvxyO1gt1Of1sENWSHXjJyd9+ohU0ZNPeda1P8LCINSEqXxbzcPuPOgSluAXDWoW9R0OnSr0OHTmbc2uViqpOoZ5duyVfnrKOI1px6LcAJBKn2c9cFofNrBoQ6JW5dIDmKi3vyLpgQynNLx4osIphmf8Pyb9GGaXDR+Q+7OEZ1JkTM/tbrVaRPHzsNDHIRl7aDBaiuXMYs2IqpNbF15uU43irm5aPc2K64hS4X8nHo0O/I5t05sO7QgcsuHfAMvb2vOPWyLefxtSe8LhztI4hKvg6USGVaj7QWUWU6GfibZ1ce5ttnHS1Lp35yABplP/PdWHfmK8LdOPOZCy8LVOTrbUYOTNGKVAc+tX9WMZ8570bMAc/Q0RRCgVV3Xh9Tb2w3Qy/QpV+GDv1ObFHMP8pZl97Oww3MnTowCc/s+S7uktcLrVMFBC/A1kWRMQk8kMW9DgxqRL8R5lbwT7Z9gnkh1E62tcJdcuzSqVKeM8U3TaxSHf8k5FXEgdOIBTh15mW3VsSYg4n2Dx36ndiqoK9GLhdcut8dpoFGS6e+zNSb561l6wDOunZ/vTCN+mwdfL5t8dSNt9P72pn52dsTwMnHP+fU2+X0GuGe3V8Ffz7455KI1/e8RciBWcwC4DRqWXS21M98wZ2f3L8h6NLPQ0G/A1sV88LNsQtwGr0AMyc8K5SWx8xWOVopmjb3rYp74YLIF1qxn22/svDGJU7WRV2K9nL7orBZX+eSiAPnO1jKaze/dGaZefPe58QceLy4pYWivg4jF3Id0yrqNVIpJPWZVkJT+GyLcMtCaaG8RolixnES9oLmpSVCmCKZWnAVX7RBxF+7CP0iSmknEmtFXEYsHnhBHy6YnrlLX3zGpfsuNM+pIt4UPqfHLYR8kYdPJwmb5+Xt8+v128WcPC506D/M1t154Vr0cvKY1qnXbZNjn0UwhaVrX66G1BZRy/WT91iJaU72u83OfyM8b1/ylqH2rfMGTnu/WxFf6UiZCflSxIHTUaDAyTwtF4ug/oCT3d66Oy/QpZ9Ch04+zdKtt0W36tgBoG2BS82JQFNeiig7bFtGPaUlxea3C00bpCzX0Zw9romMVtZiu5Sf1+ddMz7nxBo4dd2zN1+I/ZrLbpx4fdoyXmlunyt+PopQk89Dh/6DPIo7L5ztSV+ZtOvcmqMn+Xq9Y5GzA3P3Dizy9Haw01LYV1z3mkj/7sIda6yJ5Kpbv+Do29c4iW0Whc61129bElfec1XIz8Qsjyb6dOlzKOg/xKOJeeFTol44J+71/vMiffJaayM61+KTa6J9gxu/mauufUUcV1cVmr/OaSxy3uGfE/Gzr+VPOt127rEPAEV9gpEL+RxNobRuKvFHW/AEppz7QiSzFMcTcUkrIl8im9m2/B5flJV/mEu93itre64L7prDvxKp3CLk/uT1zQ8q5mQOHfoP8KjuvOUjTv3ic6659vq4c+93asZuXpTjA/O23MyNCzDfLNzA2QUorrnxs+8zvcDt+/Zg0KU7dOjkJk7cd71jIRKNwK8+pxWheH4ptIvfzsU+2LjoQTwXq/ykbn0mjilPvbis3AdE+Uo74h6EnMyhQ/9m9uDO17jqiq+sdnTx+WtFztlL3xinfEcR9Bo3iORNQ/AvTG97VYifVMjp0unQySc5GWB08oAVUVlx72tc+1back72c2x17pIrc5EDHxDdDw4K2quYE4cO/RvZqzu/xs2Z9skTv2jQzz2c+YIvE85PjuJ8VuF+dpdOQf8mnlXMz/EjIvtFJ4Qv5QeG1T+reJ/jmUWdkQv5EVrR+TZxf6I5SSjiZA069G+A7vxzbCEq2RoU7s/xrC6dDp1shmvitUfBp2CTr4QO/YuhOydkGzyjS99gFYkQQshnoKB/IXTnhGyHZ/w+UtC/iGf8n4eQrfNs30sKOiGE7AQK+hfwbC6AkEfimb6fFHRCCNkJFPTf5JnO/oQ8Ks/yPaWg/wbP8j8JIeQxoKATQp6CZzBgFPRP8gz/cxCyN/b+vaWgE0LITqCgf4K9n+UJ2TN7/v5S0AkhZCdQ0D/Ins/uhDwLe/0eU9A/wF7/JyDkGdnj95mCTgghO4GCfiN7PJsT8uzs7XtNQSeEkJ1AQb+BvZ3FCSETe/p+U9AJIWQnUNCvsKezNyFknb18zynohBCyE8RsFycmQgh5eujQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ1DQCSFkJ/wvfnoalXvx5X8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_pdf_contours(softmaxNormal3D(mu=mu1, Sigma=Sigma1, c=1.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "561\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_pdf_contours(Dirichlet(alpha1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ToRa72ll26b67tPRToV77+Ssh1aWVt3zfzsF+41A/19KBqSHQB/Rrv/KXLr4LFD8KldwF2j0OlL5uFd9ZJVFh7GFVXrJYWKroiuORvi1dOh/qfcYhA2wTcK1QZznisi2xpXMJuoH86jf/ysWrbE4eGDmr9NYoPVnISiaR7DaR3TqZ2MnG6a2JncwukUnSWzknxYWZen6bJFIimfzSdM4dLlPnEmkXH112bs+VD7yWLldXvKSddL5x7y9FV7mkXYcW605cWanmndu/b9NdxDFLEhdqSZer4xJ0A9k9DpRE6Zw8CSUZKQmy0/rzkr2T0qqdyFqjxDgZ62SMS6co20QKbRrqgeRk0mBv+yBOXVqujSBoF8pt3++E0mXsroCmjiWgoQ/gG7/+1y5emSzQjZIwDXFnjFwgyUhmJwVbp2DjZDdOdudkY8ns0oactvZEdlto6lK5re8beU1Lj+P0uqP5+51o55LqG3oX12zpXS6Q0fVjTn3aytdigqCxsTf9wqDhT8NSWjoNfQC7x1bxKg3yJDRKIskFkjPprXH5uLq64iQboe8nJTa93SWH/ViktK3H2Z+tTQO8yqTN/0hNmB9/bI9mX23p+X10aO+tWnrfYL7gAtRHd1Xc+z37c9sRTvH9gbHR0C/09d/5vkuDXPt2nkTp6+n8PB212J1kN5Ldlpu6cTrM1Hcubeixk9kmaSsvtPP9fL3a0uP4eI4ex8chXXi91NBr3t7KNVp6n3be9z5GRqjf1hJaOg39Ar/87e+7ZKVDO8+aeRJKySqbnbvDDP3g8O/KbtOPkdLcSSIrq0SSlbaJTN7OnZMz5tDSlRwKubVSkoVFU9uuC/Ojh9WxqWdt3FibhnqPln4Vxk4i1GnrGBvLFi/w+WtGn79m9PCq9PCqtH4lu33Vaf2q0+aLTi6UXN7gs7Dfvx6mq1+SIJu5hyYb02S3xbNKs73SXWH5YekydcXrjubXHG04/b+0nK/DxS9qNZ1s1GFt+pl3aP9YZoIDtLexhGWMjFx6+rm/+BuXhrPLAtpJoZNWiRQkMtbJbQMFH4cKPzUKNpLZSsE2beV2KwUbp2AjBet03GLi7OBocjx6OVrOWBy95GOWUwdHG8YvpbZYHX+0/bdRuI/S+KVjEz05fjnVsNuE/gQaehEt/XZ8Hr0wculp/RM7mTCRAicbJorCRFG0UxTGugtjOSf9+MmLitdWdh2ka9BdlpnZi4mNrHX7lm7z8YzLTy5yUmhktoVxSyBpVwk+a9Lxi7XpJwiUhrp0GH8UW7dz+/FIaeVG3pa7LidsGrF0HL2cPEg64EFOwFc09B5+/u/+3EVhrCiMtQpircKd7oKdXow2ehRsZY3Tj9f3+q9PXtazTx7LfhIpfGb3zTxt51KwTtv5IC09SdIQL55oVGzquWpjr2vq0iHUz/37KM7dBzhImmt9sLTtSGZivwho6Lfla0unoffws6//jx4FO92HGz0ONnocbHVvN7oPNrq3Gz24UB+Yr+jZ/Z3Wm1DrrZXZGpnEKHHZMsWslZvg0NJLB1HPtPTSMkYlcrIyiSscMLXlpi4dDlhKh1UwhaYu1QTNqQOlxQtpFA6GDnGQ9OySxgnM1vuefQqMhUDv6E//6Tfc11/JAtyudW/XeiF7uTcbBSbRh5sv6eO7F/Tp/Z3W21D/tw0Ub6zsJpBVGsZJkm4F4OJ0gYpJjEz+d0F2G0rGmX24G51prcXRSzHUpfpgr4S6VDh5xppuo5c2oZ7rsE5d6nAC0g0Q6vP0hn3X+djSCfQO/v5Hv+i+8eJaj8xWL9iNXjA73VunexPo3kS6M5GeJmvF7n/15O5en8Z3erq502eblZ5v0lA3z9MljkrSpm7CdJZuEpe+nqi5pTtzaOZNLT1fzpiHuoLyXL0Y4A2hvpeHet3b6lbCNIV6VV0Angj5a28T0EbxfzKE+jz5GOq3/3/rDAUmUSBXu1lhfK5FF5jiAdKsnTe+b9/rjOIquszEmZ9jLBwUbelvP/imez18ppeD57o3m31DvzNOL1ire5P+Z+cf15F+8PBT+tfPvqofPn1dHz35gp5nB0ajJyY9Y3RdOCi6cQrWUviQHgTN93exu+SwE+M2yXZjTE7v6yIV/t4dDgTmzTx/u1Q+k7Ruf5dc3YHNU230mgdG293J5fdRd7en/kdx4vtDmE+PTy2dkUtLsaw2LlAsq0RWsaweXCBrYm2d02fa6aOd1b9tvlIb5quPjYKH6ioXp3Dt0pUuD1mAuzTQSxt1bePm0/6LAZ7LV7hIx+vR87/LbmtDvPg+dQF0JpRGW4ve7Y6GuZ8+nzr7mqvBTphjbAR6C3/8g3fdF6OVHpk7reJYURDLJqECm6RbqRin54n0L5uv6oPPv6r/+PTVozCPnmVhvktv90G+ThQ8ZHuku7SRp/u2ONltLOXNPL9tauLVg575bU0Tl2raePV/atWm3aB2Tn60jPGCkHbJKPu0FMN1rPk3AT4PPs3SCfQWti7QOon0YCNtXKCtAq0UK5ZVLKPPEunD3Sv694cv68NPX9NHT18qhfnqiRQ+HG+hG66dgodYdh1nQa7DhlxJOmbRNi6fCSq1W2cu7d9WGyx1F7YoOBqZ1DGm+f0uCfNqSA/Ytpsu+MxBTfiAQD/jN//hu+4LUaTIxLqz21JLj5zVgwI9Sx7pnz//mn74/Ev672df0LOnj2WehvswXz1zsjuV9kIP1k52kyh42B12VqzsqJgG+u64hRfHKCe2x3X5LowNbz/ZwtscW2n6RaIOQX6l0ci5tkyoL5svLZ1AP2OThFonYW1Lj53Vc7fSB+uv6Eefv6b//PRl/fjpvZInK919YrV6Ij362NUGud0lsptY9vNt/Ww8D+PdrtzC8xA/Nf+W2rXv4vsVDXUA84KwbppDX3Jfbd6PUMecscoFADzBOnQA8ASBDgCeINABwBMEOgB4gkAHAE8Q6ADgCQIdADxBoAOAJwh0APAEgQ4AniDQAcATBDoAeIJABwBPEOgA4AkCHQA8QaADgCcIdADwBIEOAJ4g0AHAEwQ6AHiCQAcATxDoAOAJAh0APPH/pENtpngPkcEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "561\n"
     ]
    },
    {
     "data": {
      "image/png": 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yLzRclsGV2s+Th4VPmynYrF3IBLoTLa6XOsU635EDXujJyGLTncdevfnTv0Zqu96p79Onj40y7rLXy6ZtAdil3zzs0k8HE/od8Fl9caqs2hHFMZnrMMUSU3mYSrG6l877/31i2hXxf1jnny/SpvY6JHI1nNaRKUhtO536Xn360Cgj0E3cYyldif/BIqordYApnTwU7NDvAMlySJ61vXlP5shUI3NbaJ/MCwVTKpi825nbrO3EbR4uGZLntNdt6NEhfh696c5Dt47mz9DD9zr1nft0YH2UMd43dH0Xdhhj3Pr8Adilnx526aeDQr9xmv1aitxfQoeeytwWOpG5wBbSLIJGYdvcX5yGv50lC6GqvT8VO4Kkvci3S31oobQj9ZT0sb4k+/unH7tAeuiWAJxLvxiU+mlg5XLj+JnzsCWuUsneLEHmcQE0D315LjAhecfRxKYrH6ldJNTTsWpxChAr7WihFsD4Y0RdFq7b9foFMjzS2PQ26QJpunazT/Vy6Bhj+rHG3oNHj5I7hxHhhvmsf3a+YklGFPMMLtetzAsvc5OrjsxjtWIzL3abAVaHS+YTudPpqKJP47Fm6ST25LEmtSusJfV0pDFlr+oF2F69MKVPEqb042FCv2H8mGLeHt5fFH6+PNeNzDs1S/pn+JdtkvjAdItYP57oVJxiAcSiWRxVxoWU3yZ0q8Xfr33STRdKIWgXSbWsHXiULpKmJ8pwWvxj/QOOgN0XSMdgSicPBMcWb5Q/FX92ajGHlAVQlUBZwpUZXJHBFplf9KyC1LO2KzeFhOQtgzLvXI8Sd63cU7GL9VJvbhvXPN7cX7tmpFGZdpwxjiWmWwT40cbhUcbOGCPQjjKeYoxx3zMbcSfGq8IxxsPh73s3yGf1xamqhBS5l3lRjMrcFAJTJpciTq8ALi6GhkXQzvVQuyAsijZjjskiaXN/c197gFIzCiloF0qTRdKDqpehBVIAOx9BOsaZJl42wYmXw2H1cjisXG4QFTbeQp4PytwWrcxtEXtzhKTu36PZq2XggCIgLIQqX4NISODOeRmLgz9atPGaoB1I97fFOv+eTbWCUJn4RVI42Vy9bPrNMN1mNx5BCnSrkqHa5MJz6ZtqF0KuARP6jfFZ/+ykKMIBRH4htC9zU/m9WWwhqNN0XrZJvBlPTBZB02TepO4sJvFuYu+kdYVkRr1dSE3n1uOBSM3+L2OjjJFNKX2IbSl9G7ee0rk42oEp/TCY0G8MVRSQsmzTeR6FHufNfaViynaixRStxIH1hdBOWnfwW6VIWAB14XocXQyJvfuC5Lb1yb0ZWwx7uPQXScWhM8rYvE960gv/2a1/EfpjjLuk9CsdPcqUTm4JxoIb4k/Fn500BxDl/uChdM48F5gq9OZB6vGAoaYf73fnRfe2S0cWwxhj/wCjZoxxJKlD/Hv5ZD3Qp2N9lHFtZ8bILmOMQPdgI+BuUvpeMKV3YErfHyb0G0JVJWRWeaFXBVyZw5YZbKlhCoV6ppqFT9+fe1GbIO0oYiBJ6aq97bvx7nX4kB0OLGo/F4vhpC4uGV0MI439Pt1XLw5iQiev/Mud9lMxANpRRWBtjNF/oJGDjeJjd5LSOcJILgkjwY3w0+yvTmYVEC525mVuqqyReT1TqCuBqQSmAkwJ1OHPWLs0h/iHNN7vzZuUnlxf69WTpN7cH5K61WiSeLqHekzundPWRSmjWwO5gTS+U0oHjk/pg+95QymddGBK3w9+t94An9UXJ2E8EVUZZJ57mVfKX8Kip6mklXjlL7FWiXI2RbiUvTpmQOxxMbSz4Dkk9Zj+Bd0F0XDEaDu+iK7whxZIU5IxxkHSE2HssnHXtqNHryBoLo4eB6W+O6xcbgA1DwcQlQVsVXiZzzK/W2LlU3ldtZMsqahNgSBRN1izRMSgmUJRsWqx4bU9h8SRxgbjPWMhUK47ziguVC8OzZ4v0OKrFWkXSDtVj6A7xhhrGLXhRBidT3DL0aM7f+GT2iV5LRdHyb3COHBl/lT82afzqoSbFXClhq20l3nszMtQs5TdZG4qB1s42Nz5mqVwcM1tB5elF/g/teumdd1L5E3qXr8/3celuZ0unibVS3+B9OwpPeWQA41O+fwBeKDRcTCl7wYT+pVRVenHFIsijCf6BdBYszTJvEDnYksv7QaBHyPsjSzGw/v9B4Pfc8X6BUsrycJkBqD2Vy0AVYdF0mTiJb6fpMJWyYJpGFMcXCBNxxh7KR3J6OJBKR0YTudHLI4ewslSOk9+QQ6ECf2K/FT9xXmZ53BV7oWea9gyyDxMtDSdeQnYMsi8CMk796nc5Q7Iw+3cweUWLrdA5gAd0rkCnPavs01iH0jo/eSeLH5Che0A0gQfF0R7C6RAN6UDGEzpo3um9xlK6cBZFkfXdmHsp3R23ReHKX07TOhX4rP64vRvfwM8zeGeZrDzAmaWoV5o1LE3n7c1Sz2LQnewpfUCF+e9EucLUydK2AHRwp/Q2YbpEwfAhDLbiB8ZDPYVi/bgpNgQxIdVeFyFjl0nJ4WWVvZjKR0I3ftQl54ma4XOnundnRhHDkI6ZIRxx10VTwlHGMm5Ycy4Emo+h8xmfkRxUcLMc9Qz352v5tJMs9RzfzEzBzO3sDMLzA2ksP6SG0huIbmFyg10ES65hWQWyCwkc0DmmsQeu3R/8VVNTOVIRxWTqZX0/v7YYsOGlN6ZeAHWplQGD/vfmthHRhj3Zdue6Huw6RR1e77Rad5nYjClb4bfNVfgs/7ZqcXcy3xewFQZ6kqjnutW5jPAzHwyr2cOZuaCzOuuuAuDvKyRlzWy0iAramRFDZ0ZqMxCaQvRFtCuFXsW0rIASKRu+1LvnQQjirmZRY9VS7yO9THGplppKhesHT3aYdPiaPP4QO3Sf86hsHa5eSj1cVi5XAH9tABmFVyV+2Q+z1DPFeqZhEtywNDMwVQWmFmowiCv/MqliD/hhFI2Gbl2EHFwTmDCrodGFJxVsMbC79ui/HOiNWuBxA1dnAujiWgWP51Gs7Aaa5LOrHmsWpI9YYB2wVRcWKhNdnd0Ej5mqGL8bWDr4ihrF0I2wohxYX6q/uKPCC1L2HnhD+ufKdRzhVUq85jMK1+x6FmNcrZCnhmUeY0yr1GVK1RFjapYoSpWmBUrVHmNPDPItPWXzELnIa1nzqd1BYh2IZ27ZPQQgHLJiGK3dmnrlO4YYyelpxMxCYOLo8Dw4uiu9Pd3Sdk3pbN2uSuY0odhQr8wTW8+L2HLLPTmYTxxFubLZ2HGvHLAzEJXBtVsiapYAQC0uCaNK3HQyqdMBZ+wV0ZDRENZ/7ix4lO5FQAa1lk4p3xiztJc7BdRoZMJwCj6OP4Y03hcJB1I6YOLo/XmxdHupo5+sdZBQYbSbKxd+uOGp0rcRx5kRMi1YAS4ID/N/uokduezdhG0DgcN1VWYZql8Z+4WBqqsUVZLPFfvWBRLLIol5vkSs9z/+VS8Y5EvsciXmOUr5Mqg1DWqzF/StK6UC926T+qSOT+7HscZQ5+eHnXaP9hobUG0X8GMjTDG92uOYu1262u7MEZ2OaNR8j5r1/sH9By7FQAPMroZmNLXYUK/EJ/VF5f98DvgeQHzoUL9lKNeaCyfBKt5qFoWoWaZtzXLfLbEh9kbnop3KHFQcMhiIg8JXYV4ayFQcKiVghgHE2oEEQcVumfrtI/FYeFSgszFid99MUncaQqX5HY6vSJR2s6trW9GYkqHCwcYxQ5dCRBOON3ZhbHe8//pLil5320BjoQHGV2Gz+qL4zlIWyj0C6Gfn4GnBexThXpRYPWksVoo1EHmq6cg84WXeTZbYT5b4tP8Fd9VL4nMTXNdiUOu2kri1fjzz9VWQYnD0mggA8RoGHGwVmBEAdpbOlYvfk+XkKRVXDxEO4ESnCJB9gJ0U3e4z43ULh1i7bKJfeQbFjqPfh9CJgCFfgH+VPzZ6R++h5uXqBc56iDzJpnHOfOFBRYGxWKJebXEp+oV381e8JS9I1cmSNyntVwslFioIMza+l/jFRzekHeSu4LDOzJk2sJY67tpZX0/7BxEA7Chbgl2FnHt9rcukXlM8KnEky0CRomPp9sQ7NCjr+2TnnLqHv3QPdLJVWFKb6HQL4D68ATMZ7CLEvU8a2U+7x44hLlBMV/ief6GT9Urfph9xffFt0bcWhwyMdBoRa7FwjiFVyn884IVa6ea57whQw4DYxVqZf3JoLV4mTu/WOqUg8SU3lvojLc7tQu6MncqOdGF6u3CqMIRo0hel651puOLvUTdjC+O7dNyLvZ5f9Yi5Eag0M/MT7O/OvX9b2EXFep5DjML44lR5jPAzC3cwtcsT/N3fKpe8eP8V/xQ/oq5WgaZW+RioMRCwzXXAeDFFtBi8SZ583HfbdYIHQCsE2hlkWcmzKn7KRkRvzAqSvwYY5hykbhtQKxY+rVLIv64BtlWLcNfC5f06P75oUtPGatkOuci3bNiifPoY1xhHn0v+ANjK0zpHgr9zKgPT8DTHHbuF0FXzQFEQeYLCzs3yMIC6Mcg899X/8R3+a8decdkXkgNBS/5ldPQ8JIH0DxHGYvaaVgnsFpQOwXjlJe5ttBW2pRuvdSb08WZMI2ifCHuRmqXpktHV+yd6kXa8cW0Tj9qYXSoNz9gYXRw98VduPUfAORhodDPyH9++N9Ovv8uLITmqGdxn5Zw4NDCT7ToWY35/B2/nb/g++oFP5S/4t/KX5CL6chbwaJI5A4A32zZGT59QYE5lgCAVwNkoa7JxEKLhYS5da1Uk9Lb0cN2+iXdtGuMzmJo9NsuaX00hQ/ffRCbKpNNC6knhOcavSxM6RT62fisf3bZ7/8F9uMC9XOB1bMfUaznwCqMJ9qZhZ6vMFss8ZvFC343+4Y/zP6O/1X+DZ/0CypZNfLOQ+msY1KHwwoaBgrWKiwlQ6lWMBAYp6CTOKwSS6r+1MkRnPCtLgvPLDRZHl3qFPqZ0L/56GfOnwusnrN2RHERFkEXFrLwMv80f21k/h/VL/hj8QsqWXXkXYiBgg33ORgIvtkSGhaVrGBE+Z4cDpVaYeV0mIQZlnncC2aN+BS7+/+JTgp3I/d3PsaIUON2LOYEwt1hQfOgumWfT2HDDw6mc3IOeKToGfip+ouTp4WfalnkfqplISGZozlwqJiv8GH2hh8Xv+IP1T/wr+Xf8cfiF3xSL/ig3vAsb3hWb/66esMH9Y5ntcRcrVBJjUIMKhVSvFhUaoVSrZK+3SJXBpkyzcFIADrpveEUoTWVebzu3HC7EoV7qrS8i5xvaCadR4uej0c+gpQJ/Qyojx/gnueonwrUc4Xlk/Iyn/ve3M4N8tkKT7N3/DD/ij9U/8Afqv/Bvxf/jX/N/qdZCNXh4KECFkrgb8OPZv/qBLnUyJ1GJStY8Yue6ev69UqmLLSyWJn9ZCI2CNoN1CwxVbv1+zrv4TYn7+axDdIV4zZL+YaETcg1YEI/MT89/ZfDIh4RGqqWWZw3D735rMbT4h3fz7/hd9VX/Fj+A3/M/4Z/y3/Bs1rik3rHs6r9RQyeFfAswLNSWCgFBaASg0pqVLJCIbWXu9ThuoGWdsOuIbkfxYa3Gq1Z4uOHfBquJ/J9U/22eoMTK5PjUVM6E/qJ8el8hnqeNyesaEYU50lvXr3i++ob/qX4J36f/x3/kf83ftSvUAAKESgAWhQUBDkUcvGpeuWMP4wfDnmYerGosZQMhRisXPtP6ndltJ1F0ZuEyZqQk8CEfkL+8+P/cVjMYRZls/FWPPOQWfiTVORVjUW5xMfyDd8XX/FD8U/8mP8dP2YvqERQiSAXQS4KJTQq0cjDpZQcWgQ6CL/oTb/EA42UtPdHTprQ+wzVLjvQPyq0fxtAc5KL9Y/JHwJkM4+Y0in0E/FZ/+zk+Ql2UcEsMtQzBVP6mfO6AmzuILlBnhvM8yU+5G/4kL3hk37BJ/UCDYelc7AAzIis3t0Kb85g5RxWELw5jTeXYek03mzuLy7Hu83xYgqsrELtNGqn8FZnWBqNldGorYKxfirGWeX3SbfSHB3anKHICpQJ1004SjP06GLDffG5xiWPheu2e9tfnK9lgqcleW1DrFi2NSHW+volXRBN65N9pW+HX7u2j0u/ojlgWmavKRceJXowjyZ1Vi7Nh/MYAAAJ2ElEQVQnQn94BhZzv895UrWYCv5coJVP51WxwsfyDZ/yV/w2+4bf6q/4Tr3BhK1vIxYOK9jmqJ2VA17cCu/O4psDXqzGN5fjmy3xFv781c7w1VT41VR4sQVeTYFvdYGXusCbybA0Qeq1Rm0UTK1gawGMALW/iBFILVB1K3ExQc62dz3cVsY1ko9SV7UXuRgvcKnb50jYQ8bLOP4g8NebxVGLdg+XeH/6mr5kU3mn16M4e1M1zcjimfrzk2ydS8ieMKGfgJ+qvzj5+Az7VPp9zisFUw2n8+fiHU/5Oz5kr/gY0nnEAp2UboPgjXMbZf5iS7zHZG4LvNoCrybHN1PgzeR4MxlW1qfzVe0vXuYKzii4WgFB5GLESztK3QJqTOwDolfGhSSfJPYgfDQihz+3ZxR+X9pRvkMyT4npPD7f2O5r95H5raZzcjSPlNKZ0E+Aen4G5jOYhR9TXM2lOftQTOe6MKiKFRb5Es/ZGz5mr/ikv2GhllhCoYg7X/UWMFehd9gk82/h8g/jE/rXusC3umxk/lrnWIbKpTYK1koi8yDyWpIqRVpR1115R7mrKPMg8FTmMZUr43wytwCcgzJe5mJst2rpyzxJ52ujijGdD8k8fc7Q9TFOLPOTpnPWLWQPmNCP5Ken/3J4fmoOIqrnbTo3ZZvOy7LGoljiQxHrlq/4Tn8D4HdCXCb/FP2Uvk3mv9oKX02FN5vj3WR4Dcn8pc7xuvIyf6uzULVomFrDmpjKVRAoGrF3Enk/nYc/YVtx79Obi2vTelO1AIMy75BWLX1hRtEOVS3p63H+qmUbTOfX4VFSOoV+BJ/VF6eeFnBx86253xp3FbbFtaWDK9p0/py/42P+io/ZCz7qF+RSd97POsBAOtXLyrmNMn+xhb8Yn8r/WVd4qQu81Dne6gzvSW/eVi1Jb258IsdQd16jqV0Ge/MmsYfre/Tm/rEjenNnh5P4LlVL54vOdE6mA4V+BKoogDyH0xouV3AqbEkbTp7stINo50/OLP5coLlYVFI3uyWunPYSDyk99cFyB5n/ait8rSt8NSVebY6l1VhaPb4IuvKduavV+CJonVQqPZGLAVSoUdJF0Fir9Hvz2JGLcZfpzSObthaIcj5U5iNskznT+XV5hJTODv1APuufnX5arN3vkj2t1LvA5BqrPMNrkeOfyxJ/z2f4W77AR/2Cb7bsbIcbj/DMYVCIwdJprKCDvL3E48LniynCJEuOb3Xpb4eK5S2k804qDyLHSgErgQ4pXdXJAmgUeZrMG4mHnrx2rdRdfHy9M2+knXbmtQ21jB3vzGvbFXm/M4/3pTVLI/cdF0E3TMicK5nvLXOm87Mw9d0YKfQDUUUBqUogG9kXxfkqQy0FdqnxvszwbVnib9kci+wd1snGMxFpWKxchpXTeLEF3myOV5Pj1XiJv5ncz5cb34+/xb58pVHXGvVS+1PLWQW3EshKtR35KvTlycKnWqFJ6VHqUdgxkfvHXfNnnEFfE7lp65VBkVvbzqEPibwR8ojI+0k8FXki1ktNs5x0V0WKnBwBhX4Afyr+7NRiDuS5vwygVgDC+TVtrrDKM3zNClR5iV/en/CP1aw5kbMS1zkJdC4WK6dgncK7zYK4feqOI4jLOsMqHCDUJPGVhlkpINQpMP5AIWUEaiWQlUAvk+mVmLDrZHolyD1d5FSml8wTmTd9eRS5sU2t0hxBmoi8ETcw3pM36XxA5GMz5kM9+ZDIe4utHZGPVSsHpHKK/HaZckqn0A9AihxSFkBRwJUZkHWXIlQNuBXgslBnvCmYPMN7bvG1KLEy2qdz1e6zopVFptr9y60TLI2GcUHaRnf6cGcFxoRZchvkvVKQd+X77DhPbqUjap/O02mUpFIxgFq55uhQFaQcFztV3R1DjIudTa1iBxY74/U6SeJAtxbZNoq4qVYJ7zE6vTIg8rU0PvS6AcGerSOnzMmJELfLnC5piHudy2wGzGewTyVslcPMM7x/yvH+UVDPBKZEM7poynAi6A81ivkSEDQnmFBhn3IRL3UAcM4vkhrjD8+HQytv48cMXa38dIpN5saXIYknVUrnoJ9erdKMGYaUrZeu6cobYdtkYsW6MGve1ilR3F7mSYqOvTiwvVIBWpH3RxBTkQ8sdF6iH/cPnUHmFPlVmWJKp9D34LP64vTTE2Q+A54WcPMSdl7AzHPUlW425Ip7uJgiji8CpnIwzwZOOX8i5vRcnvC3RWJt4PdWgRU461M2UnlHgZuBLjz230OH6K/accP28V4/HvdkqVthxwOCVEzZzb4tA+n70DolXt91gRPYv1Lpv6Z90uC/NyU+faYmdVYuhzBythmxDnoJOAU4LbDaS9Rp+P76V+2nYMJJmNOJGAi87I14zxtBsymWlVCBoNkgqz+F0pF0TOC2FXi6kJlOpvQTeDMz3hsz3DadMihw4OgJFX/XCRc3/ZMG//38Q5Q4uV+Y0HckzrCqosBY5eJEYHNBPVOo5wp1JW3lUqEVuITrqntfpDmqMvbcUeRAZ6GyI/DaNY+3e7C4dXmH9O3fp1uh+I89IPCBqZS9Bb5pMgU4XY2Svq590vpzmofYiz86U0rpTOh7YpdLqLcMkmXAKocsNZTqLYqucuiVg373Uq8rQfaKgUSOVu7pQy5J4iFpp3uNt3PfyRhh4o/0aE21SsYI09ebWJe4VtzNX9K26TtN5c3jGxYygfWJlFSKQxXKUIoeqVCAnsT3nEzxD51J4ls+LiHnhgl9B/pHmEmWQy3mkMXcp/RF1X1BpnyvPtMwlUI9GzggN4jcKemk8+bhJlWjK1ugPQIzEXb3cddIW2o/fdIh9t3GQdLFxuRjN1Ie2jslXcAcTMimTe7o9d7Nc0Zeu0/63iJPipvsylRSOhP6Abh6Bff2DilyYJVBfVt/jrznUO9+wTT/Nvy94iRsEzBCvw7pvL+Dl7Wxa0IH0M5899N3JAq7NsNyah4bkaIxgLHDso7vv+VsQ4PCjq9tnnulpL3lYxNyizChb2F0/wdR0E8LyKwaXiQVARZzP6c++HoveafGjR4rj8HHYoreJC1jvJSHcA6o63Fhx9nusUpjaEfE9O3thte2T9rw0PbvSyZsckqmkNKZ0A/FWbj3941SUe9LiNrwPSIy1LYkH2M4nbcPb5HmLtLdRF1vfPiYnQWZngk5PUzohBAyEbh9LiGETAQKnRBCJgKFTgghE4FCJ4SQiUChE0LIRKDQCSFkIlDohBAyESh0QgiZCBQ6IYRMBAqdEEImAoVOCCETgUInhJCJQKETQshEoNAJIWQiUOiEEDIRKHRCCJkIFDohhEwECp0QQiYChU4IIROBQieEkIlAoRNCyESg0AkhZCJQ6IQQMhH+P+Q5+4WJLyLwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_Normal_contours(mu2, Sigma2)\n",
    "draw_pdf_contours(logitNormal3D(mu2, Sigma2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "561\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD4CAYAAAD8Zh1EAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAADAJJREFUeJzt3VuLJHcdx+Ffdc/uZrM5SAgYNASRoKjghd4pKKhJdl5AQAQFhQgKCoKiYNAb0UtfiPeC+BJ8EREUE4i5MYfN7k5XedHdM9U93dOnqu6qXz0PhBx3t6dr9jPf/PswRVVVAUD/jU59AwBohqADJCHoAEkIOkASgg6QhKDDkldGr3vqF70k6FAzj7mo00eCDpCEoMPM8iq30ukbQYdYH29Rp08EHSAJQWfwNq1wK52+EHSAJASdQdt2fVvp9IGgM1giTTaCDlvyBYCuE3QGad84izpdJugASQg6g3PoyrbS6SpBB0hC0BmUpta1lU4XCTqD0XSERZ2uEXSAJASdQWhrTVvpdImgAyQh6KTX9oq20ukKQQdIQtBJ7Vjr2UqnCwSdtI4dWVHn1AQdIAlBJ6VTrWUrnVMSdIAkBJ10Tr2ST/3rM1yCDpCEoJNKV9ZxV24HwyLopNG1iHbt9pCfoAMkIeik0NU13NXbRU6CDpCEoNN7XV/BXb995CHo9JpYwhVBhyPwhYdjEHR6q2+R7NvtpX8EHSAJQaeX+rp2+3q76QdBB0hC0Omdvq/cvt9+ukvQ6ZUsMczycdAtgg6QhKDTG9lWbbaPh9MTdIAkBJ1eyLpms35cnIagAyQh6HRe9hWb/ePjeASdThtK7IbycdIuQQdIQtDprKGt1qF9vDRP0AGSEHQ6aahrdagfN80QdDpH1GA/gg4d4wsa+xJ0OkXMptwP7EPQAZIQdDrDKl3k/mBXgg6QhKDTCdboau4XdiHonJxoQTMEHTrOFzy2JeiclFhtx/3ENgQdIAlB52Sszt24v9hE0AGSEHROwtrcj/uNmwg6RydKh3H/sY6gAyQh6ByVddkM9yOrCDpAEoLO0ViVzXJ/skzQAZIQdI7CmmyH+5U6Qad1otMu9y9zgg6QhKDTKuvxONzPRAg6QBqCTmusxuNyfyPotEJc4PgEHRLxhXTYBJ3Gicppuf+HS9ABkhB0GmUddoPrMEyCDpCEoNMYq7BbXI/hEXQaIR7d5LoMi6ADJCHoHMwK7DbXZzgEHSAJQecg1l8/uE7DIOgASQg6e7P6+sX1yk/Q2Ys49JPrlpugAyQh6OzMyus31y8vQQdIQtDZiXWXg+uYk6ADJCHobM2qy8X1zEfQ2Yrf/Dm5rrkIOkASgs5GVlxurm8egg6QhKBzI+ttGFznHASdtfwmh34RdCAifAHPQNBZyW/uYXLd+03QAZIQdK6x0obN9e8vQQdIQtBZYJ0R4fOgrwSdS34TU+fzoX8EHSAJQScirDFW83nRL4JOREQU4/GpbwJwIEEnXr31XSuMtaz0/hB0gCQEfeDm67yaTE59U+gwK70fBH3AHLWwC1HvPkEHSELQB6q+zh23sC0rvdsEHSAJQR8gZ+ccwkrvLkEfOMctkIegD4x1ThOs9G4S9AERc5ok6t0j6APmuAVyEfSBsM5pg5XeLYIOkISgD8Cqde64haZY6d0h6Mk5aoHhEPQBss5pmpXeDYKemHXOMYn66Ql6ZoXLC0Pid3xSr97+3sq15LiFNlnppyXomVXlqW8BcESCnpB1zilZ6acj6Mmsizkck6ifhqAPhHUO+Ql6Igvr3Pk5J2alH5+gAyQh6EncdHbuuIVTsdKPS9AzctwCgyToCVjndJmVfjyC3nPXYm6d00GifhyC3nPFeLz231nnMCyC3mOv3f2+1UNvWOntE/SeW1jhteMW6xyGR9B7yjqnj6z0dgl6D4k5sIqg95jjFvrISm+PoPeMdU4Got4OQc/AOgdC0HvFOicTK715gt4no+LyL1ctceschk3Qe+K1ez9YvWa81J8es9KbJeg9cBnzcvon6xxYRdD7zDonASu9OYLecWuPWmqsc/pO1Jsh6H2xfNxinQNLBL3DrHOGxEo/nKB32E3vdQ6wTNA76v4zP7xaK2uOW6xzsrHSDyPoHTSPuWAzRKK+P0HvCesc2ETQO2bhqCXi8rhlmfN1MrPS9yPoHVVf4J6qCGxD0Dvk/rM/skpgxkrfnaB3Wf24xToHNhD0jqiv85XHLTBAVvpuBL0DVh61bFjnQs9QiPr2BL1Lqso6B/Ym6Cd2/7k3qlh+CqKzc1hgpW9H0LvAN6wAGiDoJ3T/uTeuVke1YoBY53DJSt9M0E9kIeYzVjlwCEE/lVEx/fNyxMtK2GENK/1mgn4C95//8eInZbUi4o5bYCVRX0/Qu2SHde7NuYBlgn5k55/8yXRdlNX0uMU6h51Z6asJelc4OwcOJOhHdLnOb7LDOnfswpBZ6dcJ+pGcv/BTn3zQMFFfJOhHVk0m18/P58ctzs6BAwj6EVjn0B4r/YqgH0P9rHvdOt+Tc3RgTtBbdv7pn638xhVAc6z0KUE/lvqbbzW0zgHqBL1F5y/+fFrxerRbCLhjF7DSIwS9NZcxn7l8dstcw+tc1EHUBb0to9pdu+q4BaBhgt6C88/84qrgk8nic88jWjs7t9Jh2Ctd0Nu0/F2IrHOgRYLesPPP/vLae51HROvrfM5Kh+GudEFvS1l7Gf/swdCNIS+auRyiDsMk6A06f/lXV+91HrH4FMVV3wQaaM0QV7qgN+T8c7+exXwW8aq6OjOvHbcci5UOw4u6oDelKK7+uiwXI77Lg6ENHbtEiDoMjaA34Pzzv1n5QOje61zUoTFDWumC3oTx7G4sq6twV9XaB0OPHVlRh2EQ9APd/9JvZ9WujYD5i4lmb5O719l5gys9QtQZtqGsdEE/wP0vv1nFuFj8h+Xidx3q0guJRB1yE/RDLD8QWtbiPXswNCIiRkvRjy3j2vBKn/+6ws4QDWGlC/qeXvvq76vqbBQxqSIm5dX5+ezpipfHLjfYOurCDo3IHnVB31M1HkcxqT8AOrl8uuLKkK9Y6RE7HIO0EPX5ry/skIOg7+GVr/2hWrjn5ufm83U+W+qNh7KltR4h7AxH5pUu6PsoImLW8GJ+Tl5Wi89uWeXQlX75A9q7bKIO/SXoO/rON/9YVcvPbImYrvTaOp+7Fsgmo26tw16yrnRB38G3v/WnqhoXi2fnyyaTxWe/7GCvkLa81oWdrDJG/ezUN6BP3n/pTtx9bxK3JlUUkzKqs9H0rPxiFHE2jri4iLhVu0tnLygqzmb/bP5CozWNnD+YWoyWLsvGFyaN93++e1Vu/E8OiXqXnocP2RWVt3Xdyhd+9+dq9DDi3jtVPP2vhzF6OInicRmjRxdRPLqIePR4+kdZTsNeV39vl4jrgd7ybXY3xnGLV6QeFNgt4n8I8ecU/l7+Zb//pe4gC31LD168iNvvnsXDB0Xcfv9WPPFeFVFFVOUoohxFMRlH3I5pVOffILr+qtGqimJ+FFOLdjWZRIyur/qIuPbganF2dnPwY3PwN63tG6O66XjnwODfdNvEHjaz0Lfwlb++WX3w4E48fvvJuPv2KO69XcVT/34c448vYvRoEqOPLyLKMoqLcvoio/k3hY64evXo5d+X178t3dzykq+7IfTLP37lv7opiFu+10xX173Yc6gsK91C38LXX3gr/vHuS/HOM7fi0Yd34uyjIm59cBZ33y2jGlWzs/Ri+mDo2Wh6pj6Zh3t8tdTL+QuQZgGtP3hai/zKJT6uhWt0tjrCN4R+ef0uRHDVM29W/PzrFvRWQV237hsI/Y0fGwyIoG/wt7e+WL385KfiP08/G/97cCc++vAsHj0Yx8MPR3H7/XEUkzLK4mz6IOl4HMVkMj1yKcuISTV9nvpkFsxRFVEWN6/35ZjX4lQP1+rjlaXgzn/s8rNu1rzoaZ/IL9+uaz/PJsuhbyHwESLPzV4ZvV5lWOmCvsE3nngQH1f/jX8++Xy8c+/p+OjeE3FxbxSPnyri4SfGMX44iSiqqMZFFBfV9ImgRRlRFVEUZVRVFVEUVy9AmhSzsJdXS3sU07iPxotxj4iox2lN3CPmZ/H1NwurFn9s/cev+j+DdT9n3XLk2w58g8c0C18MxZ2knKEDJOGFRQBJCDpAEoIOkISgAyQh6ABJCDpAEoIOkISgAyQh6ABJCDpAEoIOkISgAyQh6ABJCDpAEoIOkISgAyQh6ABJCDpAEoIOkISgAyQh6ABJCDpAEoIOkMT/AeV005pNw/RcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_pdf_contours(Dirichlet(alpha2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "561\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_pdf_contours(softmaxNormal3D(mu=mu2, Sigma=Sigma2, c=2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_Normal_softmax(mu, sigma, nlevels=200, subdiv=5, num_samples=10000, **kwargs):\n",
    "\n",
    "    refiner = tri.UniformTriRefiner(triangle)\n",
    "    trimesh = refiner.refine_triangulation(subdiv=subdiv)\n",
    "    xys = np.array([xy2bc(xy) for xy in zip(trimesh.x, trimesh.y)])\n",
    "    t0 = time.process_time()\n",
    "    gaussian_samples = multivariate_normal.rvs(mean=mu, cov=sigma, size=num_samples)\n",
    "    softmax_gaussian_samples = np.array([softmax_transform(x) for x in gaussian_samples])\n",
    "    t1 = time.process_time()\n",
    "    time_diff = t1 - t0\n",
    "    counts = np.zeros(len(xys))\n",
    "    for x in softmax_gaussian_samples:\n",
    "        counts[argmin_norm(x, xys)] += 1\n",
    "    \n",
    "    pvals = counts/num_samples\n",
    "    \n",
    "    return(xys, pvals, time_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#check out Samples vs Dir\n",
    "def Dir_vs_True_Gaussian_KL_divergence(alpha, x_space, true_Gaussian):\n",
    "    \n",
    "    KL_div = 0\n",
    "    dir_pvals = []\n",
    "    for i, x in enumerate(x_space):\n",
    "        \n",
    "        dir_pdf = dirichlet_pdf(x, alpha)\n",
    "        dir_pvals.append(dir_pdf)\n",
    "        \n",
    "    #normalize both dists\n",
    "    dir_pvals = np.array(dir_pvals) + 1e-20\n",
    "    dir_pvals /= dir_pvals.sum()\n",
    "    for i in range(len(true_Gaussian)):\n",
    "        true_gaussian_pdf = true_Gaussian[i]\n",
    "        dir_pdf = dir_pvals[i]\n",
    "        KL_div += true_gaussian_pdf * np.log(true_gaussian_pdf/dir_pdf)\n",
    "        \n",
    "    return(KL_div)\n",
    "\n",
    "def Gaussian_samples_vs_True_Gaussian_KL_divergence(mu, Sigma, x_space, true_Gaussian, num_samples):\n",
    "    \n",
    "    KL_div = 0\n",
    "\n",
    "    _, pvals, time_diff = sample_Normal_softmax(mu, Sigma, num_samples = num_samples)\n",
    "    sm_gaussian_pvals = []\n",
    "    for i, x in enumerate(x_space):\n",
    "        \n",
    "        sm_gaussian_pdf = 1e-20 if pvals[i] == 0 else pvals[i]\n",
    "        sm_gaussian_pvals.append(sm_gaussian_pdf)\n",
    "        \n",
    "    #normalize both dists\n",
    "    sm_gaussian_pvals = np.array(sm_gaussian_pvals)\n",
    "    sm_gaussian_pvals /= sm_gaussian_pvals.sum()\n",
    "    for i in range(len(sm_gaussian_pvals)):\n",
    "        sm_gaussian_pdf = sm_gaussian_pvals[i]\n",
    "        true_gaussian_pdf = true_Gaussian[i]\n",
    "        KL_div += true_gaussian_pdf * np.log(true_gaussian_pdf/sm_gaussian_pdf)\n",
    "        \n",
    "    return(KL_div, time_diff)\n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_space, true_pvals1, _ = sample_Normal_softmax(mu1, Sigma1, num_samples = 100000)\n",
    "x_space, true_pvals2, _ = sample_Normal_softmax(mu2, Sigma2, num_samples = 100000)\n",
    "x_space, true_pvals3, _ = sample_Normal_softmax(mu3, Sigma3, num_samples = 100000)\n",
    "true_pvals1 = np.array(true_pvals1) + 1e-20\n",
    "true_pvals1 /= true_pvals1.sum()\n",
    "true_pvals2 = np.array(true_pvals2) + 1e-20\n",
    "true_pvals2 /= true_pvals2.sum()\n",
    "true_pvals3 = np.array(true_pvals3) + 1e-20\n",
    "true_pvals3 /= true_pvals3.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Gaussian_vs_Dirichlet(seeds):\n",
    "    \n",
    "    KL1_Gaussian_list = []\n",
    "    KL2_Gaussian_list = []\n",
    "    KL3_Gaussian_list = []\n",
    "    Gaussian1_timing_list = []\n",
    "    Gaussian2_timing_list = []\n",
    "    Gaussian3_timing_list = []\n",
    "    \n",
    "    for s in seeds:\n",
    "        \n",
    "        np.random.seed(s)\n",
    "        torch.manual_seed(s)\n",
    "        \n",
    "        KL1_Gaussian = []\n",
    "        KL2_Gaussian = []\n",
    "        KL3_Gaussian = []\n",
    "        KL1_Dirichlet = Dir_vs_True_Gaussian_KL_divergence(alpha1, x_space, true_pvals1)\n",
    "        KL2_Dirichlet = Dir_vs_True_Gaussian_KL_divergence(alpha2, x_space, true_pvals2)\n",
    "        KL3_Dirichlet = Dir_vs_True_Gaussian_KL_divergence(alpha3, x_space, true_pvals3)\n",
    "        Gaussian_1_timing = []\n",
    "        Gaussian_2_timing = []\n",
    "        Gaussian_3_timing = []\n",
    "\n",
    "        print(\"KL1_Dirichlet: \", KL1_Dirichlet)\n",
    "        print(\"KL2_Dirichlet: \", KL2_Dirichlet)\n",
    "        print(\"KL3_Dirichlet: \", KL3_Dirichlet)\n",
    "\n",
    "        sample_sizes = [1, 5,\n",
    "                        10, 25, 50, 75,\n",
    "                        100, 250, 500, 750,\n",
    "                        1000, 2500, 5000, 7500,\n",
    "                        10000, 25000, 50000, 75000,\n",
    "                        100000]\n",
    "\n",
    "        for s in sample_sizes:\n",
    "            Gaussian_samples_KL_div1, time1 = Gaussian_samples_vs_True_Gaussian_KL_divergence(mu1, Sigma1, x_space, true_pvals1, num_samples=s)\n",
    "            Gaussian_samples_KL_div2, time2 = Gaussian_samples_vs_True_Gaussian_KL_divergence(mu2, Sigma2, x_space, true_pvals2, num_samples=s)\n",
    "            Gaussian_samples_KL_div3, time3 = Gaussian_samples_vs_True_Gaussian_KL_divergence(mu3, Sigma3, x_space, true_pvals3, num_samples=s)\n",
    "            KL1_Gaussian.append(Gaussian_samples_KL_div1)\n",
    "            KL2_Gaussian.append(Gaussian_samples_KL_div2)\n",
    "            KL3_Gaussian.append(Gaussian_samples_KL_div3)\n",
    "            Gaussian_1_timing.append(time1)\n",
    "            Gaussian_2_timing.append(time2)\n",
    "            Gaussian_3_timing.append(time3)\n",
    "            print(\"Gaussian_samples_KL_div1: \", Gaussian_samples_KL_div1)\n",
    "            print(\"Gaussian_samples_KL_div2: \", Gaussian_samples_KL_div2)\n",
    "            print(\"Gaussian_samples_KL_div3: \", Gaussian_samples_KL_div3)\n",
    "            print(\"time1: \", time1)\n",
    "            print(\"time2: \", time2)\n",
    "            print(\"time3: \", time3)\n",
    "            \n",
    "        KL1_Gaussian_list.append(np.array(KL1_Gaussian))\n",
    "        KL2_Gaussian_list.append(np.array(KL2_Gaussian))\n",
    "        KL3_Gaussian_list.append(np.array(KL3_Gaussian))\n",
    "        Gaussian1_timing_list.append(np.array(Gaussian_1_timing))\n",
    "        Gaussian2_timing_list.append(np.array(Gaussian_2_timing))\n",
    "        Gaussian3_timing_list.append(np.array(Gaussian_3_timing))\n",
    "        \n",
    "    print(KL1_Gaussian_list)\n",
    "    KL1_Gaussian_mean = np.mean(KL1_Gaussian_list, axis=0)\n",
    "    KL2_Gaussian_mean = np.mean(KL2_Gaussian_list, axis=0)\n",
    "    KL3_Gaussian_mean = np.mean(KL3_Gaussian_list, axis=0)\n",
    "    Gaussian1_timing_mean = np.mean(Gaussian1_timing_list, axis=0)\n",
    "    Gaussian2_timing_mean = np.mean(Gaussian2_timing_list, axis=0)\n",
    "    Gaussian3_timing_mean = np.mean(Gaussian3_timing_list, axis=0)\n",
    "    KL1_Gaussian_std = np.std(KL1_Gaussian_list, axis=0)\n",
    "    KL2_Gaussian_std = np.std(KL2_Gaussian_list, axis=0)\n",
    "    KL3_Gaussian_std = np.std(KL3_Gaussian_list, axis=0)\n",
    "    Gaussian1_timing_std = np.std(Gaussian1_timing_list, axis=0)\n",
    "    Gaussian2_timing_std = np.std(Gaussian2_timing_list, axis=0)\n",
    "    Gaussian3_timing_std = np.std(Gaussian3_timing_list, axis=0)\n",
    "    \n",
    "    return(KL1_Gaussian_mean, \n",
    "           KL2_Gaussian_mean,\n",
    "           KL3_Gaussian_mean,\n",
    "           KL1_Gaussian_std,\n",
    "           KL2_Gaussian_std,\n",
    "           KL3_Gaussian_std,\n",
    "           KL1_Dirichlet,\n",
    "           KL2_Dirichlet,\n",
    "           KL3_Dirichlet,\n",
    "           Gaussian1_timing_mean,\n",
    "           Gaussian2_timing_mean,\n",
    "           Gaussian3_timing_mean,\n",
    "           Gaussian1_timing_std,\n",
    "           Gaussian2_timing_std,\n",
    "           Gaussian3_timing_std)\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KL1_Dirichlet:  0.08817099700242213\n",
      "KL2_Dirichlet:  0.7075459257046993\n",
      "KL3_Dirichlet:  1.7655057604949025\n",
      "Gaussian_samples_KL_div1:  41.37227028232162\n",
      "Gaussian_samples_KL_div2:  43.0508627605988\n",
      "Gaussian_samples_KL_div3:  42.93349488395003\n",
      "time1:  0.000342875000001186\n",
      "time2:  0.0003325560000035921\n",
      "time3:  0.0003726260000007642\n",
      "Gaussian_samples_KL_div1:  38.94362447906433\n",
      "Gaussian_samples_KL_div2:  37.67081816574378\n",
      "Gaussian_samples_KL_div3:  38.68437050404743\n",
      "time1:  0.000342710999994722\n",
      "time2:  0.0003435869999961483\n",
      "time3:  0.0003807750000035526\n",
      "Gaussian_samples_KL_div1:  36.53962947879275\n",
      "Gaussian_samples_KL_div2:  32.05606146260672\n",
      "Gaussian_samples_KL_div3:  36.033002491131484\n",
      "time1:  0.00040833799999973053\n",
      "time2:  0.00039164300000038565\n",
      "time3:  0.00043321899999426705\n",
      "Gaussian_samples_KL_div1:  28.02311749088691\n",
      "Gaussian_samples_KL_div2:  21.566603518298848\n",
      "Gaussian_samples_KL_div3:  26.184336530157342\n",
      "time1:  0.0006157749999999851\n",
      "time2:  0.0005259759999987068\n",
      "time3:  0.0005072929999982989\n",
      "Gaussian_samples_KL_div1:  22.19309195404947\n",
      "Gaussian_samples_KL_div2:  14.698918487323569\n",
      "Gaussian_samples_KL_div3:  18.926358708561562\n",
      "time1:  0.0007642509999996605\n",
      "time2:  0.0007438549999960742\n",
      "time3:  0.0007459950000026083\n",
      "Gaussian_samples_KL_div1:  17.432575306904234\n",
      "Gaussian_samples_KL_div2:  13.053894481773213\n",
      "Gaussian_samples_KL_div3:  13.836769813381633\n",
      "time1:  0.0009230980000012323\n",
      "time2:  0.0009309010000038143\n",
      "time3:  0.0010422999999946114\n",
      "Gaussian_samples_KL_div1:  11.389084038311973\n",
      "Gaussian_samples_KL_div2:  9.845942515131538\n",
      "Gaussian_samples_KL_div3:  8.83192463272503\n",
      "time1:  0.001201786000002869\n",
      "time2:  0.0011954759999994735\n",
      "time3:  0.0012128039999979023\n",
      "Gaussian_samples_KL_div1:  6.060964352902489\n",
      "Gaussian_samples_KL_div2:  6.898683477462917\n",
      "Gaussian_samples_KL_div3:  2.4840982674859\n",
      "time1:  0.0025221550000011916\n",
      "time2:  0.002459772000001692\n",
      "time3:  0.002620358999998018\n",
      "Gaussian_samples_KL_div1:  3.1202677349265646\n",
      "Gaussian_samples_KL_div2:  4.213026711443317\n",
      "Gaussian_samples_KL_div3:  1.3216782119482622\n",
      "time1:  0.005626183000003948\n",
      "time2:  0.00531548099999668\n",
      "time3:  0.004582778999996151\n",
      "Gaussian_samples_KL_div1:  1.999732405299412\n",
      "Gaussian_samples_KL_div2:  2.971510765338571\n",
      "Gaussian_samples_KL_div3:  0.6918617208235424\n",
      "time1:  0.007585030999997855\n",
      "time2:  0.006857381999999745\n",
      "time3:  0.007977152000002263\n",
      "Gaussian_samples_KL_div1:  1.2968174200515517\n",
      "Gaussian_samples_KL_div2:  2.523873402286158\n",
      "Gaussian_samples_KL_div3:  0.6142984711187615\n",
      "time1:  0.008466038999998204\n",
      "time2:  0.00881439399999806\n",
      "time3:  0.008615167999998619\n",
      "Gaussian_samples_KL_div1:  0.4620139899508285\n",
      "Gaussian_samples_KL_div2:  1.124221060864696\n",
      "Gaussian_samples_KL_div3:  0.19811709198821686\n",
      "time1:  0.02109412000000077\n",
      "time2:  0.02081998300000265\n",
      "time3:  0.020794578000000286\n",
      "Gaussian_samples_KL_div1:  0.26647488607425274\n",
      "Gaussian_samples_KL_div2:  0.5168804814063005\n",
      "Gaussian_samples_KL_div3:  0.08017111664204754\n",
      "time1:  0.043358304000001624\n",
      "time2:  0.04091118399999516\n",
      "time3:  0.04163486099999858\n",
      "Gaussian_samples_KL_div1:  0.1442606951403442\n",
      "Gaussian_samples_KL_div2:  0.36555214275909287\n",
      "Gaussian_samples_KL_div3:  0.0669887638765397\n",
      "time1:  0.12409121199999618\n",
      "time2:  0.124646331000001\n",
      "time3:  0.12315164600000372\n",
      "Gaussian_samples_KL_div1:  0.08626120754818403\n",
      "Gaussian_samples_KL_div2:  0.27572515038614226\n",
      "Gaussian_samples_KL_div3:  0.04964957480296761\n",
      "time1:  0.16463868399999626\n",
      "time2:  0.17960971400000147\n",
      "time3:  0.16708259499999656\n",
      "Gaussian_samples_KL_div1:  0.04099310772506423\n",
      "Gaussian_samples_KL_div2:  0.09327060730438433\n",
      "Gaussian_samples_KL_div3:  0.016851249645901522\n",
      "time1:  0.4167397360000038\n",
      "time2:  0.41916408499999847\n",
      "time3:  0.409416813\n",
      "Gaussian_samples_KL_div1:  0.018897939204719758\n",
      "Gaussian_samples_KL_div2:  0.0480789676824193\n",
      "Gaussian_samples_KL_div3:  0.010526741644953461\n",
      "time1:  0.6232861760000006\n",
      "time2:  0.6171023870000028\n",
      "time3:  0.6175316409999994\n",
      "Gaussian_samples_KL_div1:  0.014946654647523257\n",
      "Gaussian_samples_KL_div2:  0.023421403080620528\n",
      "Gaussian_samples_KL_div3:  0.007676428967988868\n",
      "time1:  0.8658563279999996\n",
      "time2:  0.8236870910000036\n",
      "time3:  0.8417897340000025\n",
      "Gaussian_samples_KL_div1:  0.011107110810884634\n",
      "Gaussian_samples_KL_div2:  0.015100345061615363\n",
      "Gaussian_samples_KL_div3:  0.00489622209433406\n",
      "time1:  1.054917052999997\n",
      "time2:  1.0428431750000016\n",
      "time3:  1.0961607010000023\n",
      "KL1_Dirichlet:  0.08817099700242213\n",
      "KL2_Dirichlet:  0.7075459257046993\n",
      "KL3_Dirichlet:  1.7655057604949025\n",
      "Gaussian_samples_KL_div1:  41.37227028232162\n",
      "Gaussian_samples_KL_div2:  43.0508627605988\n",
      "Gaussian_samples_KL_div3:  42.93349488395003\n",
      "time1:  0.0003337819999984504\n",
      "time2:  0.0003224470000020574\n",
      "time3:  0.0003425869999915676\n",
      "Gaussian_samples_KL_div1:  39.09695028968303\n",
      "Gaussian_samples_KL_div2:  31.47298514737043\n",
      "Gaussian_samples_KL_div3:  37.981738311038285\n",
      "time1:  0.0003337609999931601\n",
      "time2:  0.00036979600000108803\n",
      "time3:  0.00035672399999953086\n",
      "Gaussian_samples_KL_div1:  36.986745452150345\n",
      "Gaussian_samples_KL_div2:  34.163076535596865\n",
      "Gaussian_samples_KL_div3:  33.84760634715139\n",
      "time1:  0.000383921999997483\n",
      "time2:  0.00046032800000261886\n",
      "time3:  0.0004232400000034886\n",
      "Gaussian_samples_KL_div1:  30.31611868083405\n",
      "Gaussian_samples_KL_div2:  24.57248867308747\n",
      "Gaussian_samples_KL_div3:  24.492223426740455\n",
      "time1:  0.0005261040000021922\n",
      "time2:  0.0005542720000022427\n",
      "time3:  0.0005159499999933814\n",
      "Gaussian_samples_KL_div1:  24.88243339659095\n",
      "Gaussian_samples_KL_div2:  16.86437795987338\n",
      "Gaussian_samples_KL_div3:  19.624566558317635\n",
      "time1:  0.0007338479999958736\n",
      "time2:  0.0007518000000032998\n",
      "time3:  0.0007558410000001459\n",
      "Gaussian_samples_KL_div1:  16.214320294449372\n",
      "Gaussian_samples_KL_div2:  10.994579022961664\n",
      "Gaussian_samples_KL_div3:  15.560840664568868\n",
      "time1:  0.0009407560000056492\n",
      "time2:  0.0009417129999889085\n",
      "time3:  0.0019902400000120224\n",
      "Gaussian_samples_KL_div1:  15.132899871966098\n",
      "Gaussian_samples_KL_div2:  9.55727742184804\n",
      "Gaussian_samples_KL_div3:  7.371575289837215\n",
      "time1:  0.0011771289999984447\n",
      "time2:  0.0011279320000028292\n",
      "time3:  0.0011925759999940055\n",
      "Gaussian_samples_KL_div1:  6.1050772980307695\n",
      "Gaussian_samples_KL_div2:  7.025113055693366\n",
      "Gaussian_samples_KL_div3:  4.305264332822872\n",
      "time1:  0.002379278999995904\n",
      "time2:  0.002441750000002685\n",
      "time3:  0.0023566670000008116\n",
      "Gaussian_samples_KL_div1:  3.7305234411398946\n",
      "Gaussian_samples_KL_div2:  4.338146237499269\n",
      "Gaussian_samples_KL_div3:  1.2244162058337116\n",
      "time1:  0.005222563999993213\n",
      "time2:  0.004419926000011287\n",
      "time3:  0.0047006010000103515\n",
      "Gaussian_samples_KL_div1:  1.9899764374809155\n",
      "Gaussian_samples_KL_div2:  2.6770566940726073\n",
      "Gaussian_samples_KL_div3:  0.895490190967863\n",
      "time1:  0.006309479000009333\n",
      "time2:  0.006400873000004026\n",
      "time3:  0.00645333200000664\n",
      "Gaussian_samples_KL_div1:  1.1701100935068058\n",
      "Gaussian_samples_KL_div2:  2.286578093614835\n",
      "Gaussian_samples_KL_div3:  0.3473797932635794\n",
      "time1:  0.008576766000004454\n",
      "time2:  0.008731239999988816\n",
      "time3:  0.00842608899999675\n",
      "Gaussian_samples_KL_div1:  0.42120824225298337\n",
      "Gaussian_samples_KL_div2:  1.0521317737043367\n",
      "Gaussian_samples_KL_div3:  0.20054013260671824\n",
      "time1:  0.020760492999997382\n",
      "time2:  0.021056923999992705\n",
      "time3:  0.02072915600000158\n",
      "Gaussian_samples_KL_div1:  0.22932484192779684\n",
      "Gaussian_samples_KL_div2:  0.4994356902702392\n",
      "Gaussian_samples_KL_div3:  0.12145544496960956\n",
      "time1:  0.04138908900000615\n",
      "time2:  0.042014710000003674\n",
      "time3:  0.0424590639999991\n",
      "Gaussian_samples_KL_div1:  0.14963284370300767\n",
      "Gaussian_samples_KL_div2:  0.4229039557091823\n",
      "Gaussian_samples_KL_div3:  0.06110651247267373\n",
      "time1:  0.12496748800001001\n",
      "time2:  0.12332640699999331\n",
      "time3:  0.12277958199999262\n",
      "Gaussian_samples_KL_div1:  0.08537341470159569\n",
      "Gaussian_samples_KL_div2:  0.21200856593393463\n",
      "Gaussian_samples_KL_div3:  0.07091952042408212\n",
      "time1:  0.16527167200000292\n",
      "time2:  0.16493467600000145\n",
      "time3:  0.16741360199999633\n",
      "Gaussian_samples_KL_div1:  0.03629515555780785\n",
      "Gaussian_samples_KL_div2:  0.0989558438749408\n",
      "Gaussian_samples_KL_div3:  0.02534563798585137\n",
      "time1:  0.4135465899999957\n",
      "time2:  0.4152679839999962\n",
      "time3:  0.40639495000000636\n",
      "Gaussian_samples_KL_div1:  0.024643253097160266\n",
      "Gaussian_samples_KL_div2:  0.03811208661123165\n",
      "Gaussian_samples_KL_div3:  0.008403527255316554\n",
      "time1:  0.6222322290000051\n",
      "time2:  0.6158111649999967\n",
      "time3:  0.6205441620000016\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian_samples_KL_div1:  0.013150703206418453\n",
      "Gaussian_samples_KL_div2:  0.022667884180506227\n",
      "Gaussian_samples_KL_div3:  0.009683519000104794\n",
      "time1:  0.8403424790000003\n",
      "time2:  0.833055518000009\n",
      "time3:  0.8281476599999991\n",
      "Gaussian_samples_KL_div1:  0.010539190034223364\n",
      "Gaussian_samples_KL_div2:  0.016825734223673852\n",
      "Gaussian_samples_KL_div3:  0.004284839024513732\n",
      "time1:  1.0445630140000048\n",
      "time2:  1.0420133019999867\n",
      "time3:  1.0454667439999952\n",
      "KL1_Dirichlet:  0.08817099700242213\n",
      "KL2_Dirichlet:  0.7075459257046993\n",
      "KL3_Dirichlet:  1.7655057604949025\n",
      "Gaussian_samples_KL_div1:  41.37227028232162\n",
      "Gaussian_samples_KL_div2:  43.0508627605988\n",
      "Gaussian_samples_KL_div3:  42.93349488395003\n",
      "time1:  0.00036971699999810426\n",
      "time2:  0.0003285549999958448\n",
      "time3:  0.00034152899999639885\n",
      "Gaussian_samples_KL_div1:  38.9702898374328\n",
      "Gaussian_samples_KL_div2:  36.5859825027866\n",
      "Gaussian_samples_KL_div3:  36.93290088187853\n",
      "time1:  0.00034728800000038973\n",
      "time2:  0.0003649740000071233\n",
      "time3:  0.0003750580000030368\n",
      "Gaussian_samples_KL_div1:  36.59300340124835\n",
      "Gaussian_samples_KL_div2:  28.947469203902923\n",
      "Gaussian_samples_KL_div3:  34.412040229029294\n",
      "time1:  0.00037213200000962843\n",
      "time2:  0.000415165000006823\n",
      "time3:  0.0004182009999880165\n",
      "Gaussian_samples_KL_div1:  31.328213520272183\n",
      "Gaussian_samples_KL_div2:  16.212080057846382\n",
      "Gaussian_samples_KL_div3:  23.846890365210538\n",
      "time1:  0.0005131050000102277\n",
      "time2:  0.0005184059999976398\n",
      "time3:  0.0005420549999968216\n",
      "Gaussian_samples_KL_div1:  23.2525842189568\n",
      "Gaussian_samples_KL_div2:  13.689966570355223\n",
      "Gaussian_samples_KL_div3:  18.30995008636459\n",
      "time1:  0.0007545389999989993\n",
      "time2:  0.0007353420000129063\n",
      "time3:  0.0007451559999935853\n",
      "Gaussian_samples_KL_div1:  17.57645458898396\n",
      "Gaussian_samples_KL_div2:  10.441438548206992\n",
      "Gaussian_samples_KL_div3:  12.517568079306264\n",
      "time1:  0.0009607829999964679\n",
      "time2:  0.0009593869999946492\n",
      "time3:  0.0009818260000002965\n",
      "Gaussian_samples_KL_div1:  13.485568679447939\n",
      "Gaussian_samples_KL_div2:  9.630398582240042\n",
      "Gaussian_samples_KL_div3:  8.431938302957642\n",
      "time1:  0.0011575750000076823\n",
      "time2:  0.0011352840000000697\n",
      "time3:  0.001133980000005863\n",
      "Gaussian_samples_KL_div1:  5.431922866658652\n",
      "Gaussian_samples_KL_div2:  5.4520928845132035\n",
      "Gaussian_samples_KL_div3:  3.5741317373200214\n",
      "time1:  0.0023260290000024497\n",
      "time2:  0.0023718269999903896\n",
      "time3:  0.0023694489999996904\n",
      "Gaussian_samples_KL_div1:  2.3795283801654894\n",
      "Gaussian_samples_KL_div2:  4.18783048322008\n",
      "Gaussian_samples_KL_div3:  0.9971913238428691\n",
      "time1:  0.005059922000000938\n",
      "time2:  0.004378559000002724\n",
      "time3:  0.004691747000009627\n",
      "Gaussian_samples_KL_div1:  1.6809206897926836\n",
      "Gaussian_samples_KL_div2:  3.7565434697237614\n",
      "Gaussian_samples_KL_div3:  0.8085553965252927\n",
      "time1:  0.006445103999993762\n",
      "time2:  0.006382103999996502\n",
      "time3:  0.006440515999997842\n",
      "Gaussian_samples_KL_div1:  1.0693616539331168\n",
      "Gaussian_samples_KL_div2:  2.380157451619123\n",
      "Gaussian_samples_KL_div3:  0.2647601777377162\n",
      "time1:  0.00843005999999491\n",
      "time2:  0.008352188999992904\n",
      "time3:  0.008296505999993542\n",
      "Gaussian_samples_KL_div1:  0.5328095866629011\n",
      "Gaussian_samples_KL_div2:  1.3592038719607442\n",
      "Gaussian_samples_KL_div3:  0.17121277297969587\n",
      "time1:  0.02102812300000778\n",
      "time2:  0.021071825999996463\n",
      "time3:  0.021286634999995613\n",
      "Gaussian_samples_KL_div1:  0.26759631443766907\n",
      "Gaussian_samples_KL_div2:  0.517813590856059\n",
      "Gaussian_samples_KL_div3:  0.08817711340625038\n",
      "time1:  0.0411266290000043\n",
      "time2:  0.04076413900000375\n",
      "time3:  0.04234844500000179\n",
      "Gaussian_samples_KL_div1:  0.16818507499342145\n",
      "Gaussian_samples_KL_div2:  0.3243381978855842\n",
      "Gaussian_samples_KL_div3:  0.05617826383844964\n",
      "time1:  0.12407242300000121\n",
      "time2:  0.12203197700000601\n",
      "time3:  0.12429685899999754\n",
      "Gaussian_samples_KL_div1:  0.11576355884600864\n",
      "Gaussian_samples_KL_div2:  0.3094544195966304\n",
      "Gaussian_samples_KL_div3:  0.04088453206141117\n",
      "time1:  0.19125127499999905\n",
      "time2:  0.17446080899999572\n",
      "time3:  0.16715058399999805\n",
      "Gaussian_samples_KL_div1:  0.03850896380473137\n",
      "Gaussian_samples_KL_div2:  0.10241284003236518\n",
      "Gaussian_samples_KL_div3:  0.02768931601264085\n",
      "time1:  0.4111819789999913\n",
      "time2:  0.40685113099999626\n",
      "time3:  0.40657378999999594\n",
      "Gaussian_samples_KL_div1:  0.021590147698582415\n",
      "Gaussian_samples_KL_div2:  0.04053114038901287\n",
      "Gaussian_samples_KL_div3:  0.009653924013555725\n",
      "time1:  0.6214531409999893\n",
      "time2:  0.6158387569999917\n",
      "time3:  0.615034640999994\n",
      "Gaussian_samples_KL_div1:  0.019421938374647146\n",
      "Gaussian_samples_KL_div2:  0.02298515442514221\n",
      "Gaussian_samples_KL_div3:  0.0069754857280331884\n",
      "time1:  0.8341307350000022\n",
      "time2:  0.825113131000009\n",
      "time3:  0.824142806999987\n",
      "Gaussian_samples_KL_div1:  0.012538425042540869\n",
      "Gaussian_samples_KL_div2:  0.022081683728445798\n",
      "Gaussian_samples_KL_div3:  0.0068889148461761885\n",
      "time1:  1.0464719709999883\n",
      "time2:  1.0399108469999874\n",
      "time3:  1.0403356069999745\n",
      "KL1_Dirichlet:  0.08817099700242213\n",
      "KL2_Dirichlet:  0.7075459257046993\n",
      "KL3_Dirichlet:  1.7655057604949025\n",
      "Gaussian_samples_KL_div1:  41.37227028232162\n",
      "Gaussian_samples_KL_div2:  43.0508627605988\n",
      "Gaussian_samples_KL_div3:  42.93349488395003\n",
      "time1:  0.000338881000004676\n",
      "time2:  0.0003295870000101786\n",
      "time3:  0.00033889599998815356\n",
      "Gaussian_samples_KL_div1:  38.731639611301475\n",
      "Gaussian_samples_KL_div2:  33.646126742663\n",
      "Gaussian_samples_KL_div3:  38.28309255153131\n",
      "time1:  0.00034627200000159064\n",
      "time2:  0.0003427710000210027\n",
      "time3:  0.00036698300002058204\n",
      "Gaussian_samples_KL_div1:  34.64704268745724\n",
      "Gaussian_samples_KL_div2:  35.08074676122491\n",
      "Gaussian_samples_KL_div3:  35.21782868429028\n",
      "time1:  0.00040911600001436454\n",
      "time2:  0.0004425390000051266\n",
      "time3:  0.0004359719999911249\n",
      "Gaussian_samples_KL_div1:  31.4535127757689\n",
      "Gaussian_samples_KL_div2:  20.031690084522527\n",
      "Gaussian_samples_KL_div3:  26.1212856874776\n",
      "time1:  0.0005239870000082192\n",
      "time2:  0.0004993549999880997\n",
      "time3:  0.0005265270000052169\n",
      "Gaussian_samples_KL_div1:  22.833373231157488\n",
      "Gaussian_samples_KL_div2:  14.833153763873229\n",
      "Gaussian_samples_KL_div3:  19.362521978910433\n",
      "time1:  0.00074997799998755\n",
      "time2:  0.0008256929999959084\n",
      "time3:  0.0007376979999946798\n",
      "Gaussian_samples_KL_div1:  17.60117302272889\n",
      "Gaussian_samples_KL_div2:  12.066140219557296\n",
      "Gaussian_samples_KL_div3:  9.542067863908915\n",
      "time1:  0.000994195999993508\n",
      "time2:  0.0009373409999966498\n",
      "time3:  0.0016049189999876035\n",
      "Gaussian_samples_KL_div1:  15.190090153466594\n",
      "Gaussian_samples_KL_div2:  10.154395087420282\n",
      "Gaussian_samples_KL_div3:  10.232154792370045\n",
      "time1:  0.001152316000002429\n",
      "time2:  0.001145264000001589\n",
      "time3:  0.0011757279999926595\n",
      "Gaussian_samples_KL_div1:  6.400628275917653\n",
      "Gaussian_samples_KL_div2:  5.820761990629291\n",
      "Gaussian_samples_KL_div3:  3.6362231374206613\n",
      "time1:  0.0028602250000062668\n",
      "time2:  0.0023419399999795587\n",
      "time3:  0.002398635000020022\n",
      "Gaussian_samples_KL_div1:  2.4127864882151684\n",
      "Gaussian_samples_KL_div2:  4.035420918759406\n",
      "Gaussian_samples_KL_div3:  1.0221247616902391\n",
      "time1:  0.005414287000007789\n",
      "time2:  0.004537538000022323\n",
      "time3:  0.004555400000015197\n",
      "Gaussian_samples_KL_div1:  1.4183553949616523\n",
      "Gaussian_samples_KL_div2:  2.8776923129930605\n",
      "Gaussian_samples_KL_div3:  0.459325806721241\n",
      "time1:  0.006488496000002897\n",
      "time2:  0.006249478000000863\n",
      "time3:  0.006778808000007075\n",
      "Gaussian_samples_KL_div1:  1.235987357513661\n",
      "Gaussian_samples_KL_div2:  2.3953261281362916\n",
      "Gaussian_samples_KL_div3:  0.5779481352982581\n",
      "time1:  0.00849236099998052\n",
      "time2:  0.008540863999996873\n",
      "time3:  0.008450073999995311\n",
      "Gaussian_samples_KL_div1:  0.42652504476908626\n",
      "Gaussian_samples_KL_div2:  1.2307841357337472\n",
      "Gaussian_samples_KL_div3:  0.27581645243288505\n",
      "time1:  0.021390857000000096\n",
      "time2:  0.020707290000018475\n",
      "time3:  0.020744703000019626\n",
      "Gaussian_samples_KL_div1:  0.2874233221214743\n",
      "Gaussian_samples_KL_div2:  0.5071380855788703\n",
      "Gaussian_samples_KL_div3:  0.10179558651966529\n",
      "time1:  0.04215348900001459\n",
      "time2:  0.04147427199998788\n",
      "time3:  0.041694751000022734\n",
      "Gaussian_samples_KL_div1:  0.16480437091855013\n",
      "Gaussian_samples_KL_div2:  0.3488677119659843\n",
      "Gaussian_samples_KL_div3:  0.06133956105583948\n",
      "time1:  0.12609240599999794\n",
      "time2:  0.1815417570000193\n",
      "time3:  0.14179144500002394\n",
      "Gaussian_samples_KL_div1:  0.09826545869827677\n",
      "Gaussian_samples_KL_div2:  0.2625215369640883\n",
      "Gaussian_samples_KL_div3:  0.054741755691282125\n",
      "time1:  0.1689875559999905\n",
      "time2:  0.16909059099998558\n",
      "time3:  0.16762091200001805\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gaussian_samples_KL_div1:  0.035533164968865605\n",
      "Gaussian_samples_KL_div2:  0.09663596855558308\n",
      "Gaussian_samples_KL_div3:  0.019666059213918983\n",
      "time1:  0.4176054840000063\n",
      "time2:  0.40557112699997333\n",
      "time3:  0.4057970629999943\n",
      "Gaussian_samples_KL_div1:  0.021347980484659614\n",
      "Gaussian_samples_KL_div2:  0.042211753526617754\n",
      "Gaussian_samples_KL_div3:  0.007536274939427632\n",
      "time1:  0.6259354169999938\n",
      "time2:  0.6176461689999826\n",
      "time3:  0.6169133759999852\n",
      "Gaussian_samples_KL_div1:  0.013589491323716101\n",
      "Gaussian_samples_KL_div2:  0.025157194184984376\n",
      "Gaussian_samples_KL_div3:  0.007154872699209303\n",
      "time1:  0.8398047880000092\n",
      "time2:  0.8276589589999901\n",
      "time3:  0.8258046200000138\n",
      "Gaussian_samples_KL_div1:  0.00938493657803245\n",
      "Gaussian_samples_KL_div2:  0.018862321359728557\n",
      "Gaussian_samples_KL_div3:  0.006862983752319675\n",
      "time1:  1.0399479210000209\n",
      "time2:  1.0441900689999954\n",
      "time3:  1.050983954000003\n",
      "KL1_Dirichlet:  0.08817099700242213\n",
      "KL2_Dirichlet:  0.7075459257046993\n",
      "KL3_Dirichlet:  1.7655057604949025\n",
      "Gaussian_samples_KL_div1:  41.37227028232162\n",
      "Gaussian_samples_KL_div2:  43.0508627605988\n",
      "Gaussian_samples_KL_div3:  42.93349488395003\n",
      "time1:  0.00035324200001696227\n",
      "time2:  0.0003276829999947495\n",
      "time3:  0.0003596969999932753\n",
      "Gaussian_samples_KL_div1:  38.963623497840686\n",
      "Gaussian_samples_KL_div2:  39.31118212804403\n",
      "Gaussian_samples_KL_div3:  36.99245351556811\n",
      "time1:  0.00033670400000573864\n",
      "time2:  0.0003611310000053436\n",
      "time3:  0.0003757210000117084\n",
      "Gaussian_samples_KL_div1:  35.73464573028205\n",
      "Gaussian_samples_KL_div2:  29.073288583570257\n",
      "Gaussian_samples_KL_div3:  36.11643554268213\n",
      "time1:  0.00038921399999480855\n",
      "time2:  0.0004395979999856081\n",
      "time3:  0.0004138199999772496\n",
      "Gaussian_samples_KL_div1:  30.767886066480674\n",
      "Gaussian_samples_KL_div2:  22.26926549165397\n",
      "Gaussian_samples_KL_div3:  26.618824593997253\n",
      "time1:  0.0005810789999998178\n",
      "time2:  0.0005148609999992004\n",
      "time3:  0.0005445840000106728\n",
      "Gaussian_samples_KL_div1:  20.498841429150005\n",
      "Gaussian_samples_KL_div2:  17.088401885528224\n",
      "Gaussian_samples_KL_div3:  19.54875624589249\n",
      "time1:  0.0007634520000010525\n",
      "time2:  0.0007167249999895375\n",
      "time3:  0.0007548090000000229\n",
      "Gaussian_samples_KL_div1:  16.98277275925966\n",
      "Gaussian_samples_KL_div2:  11.61394723500469\n",
      "Gaussian_samples_KL_div3:  11.870234075661815\n",
      "time1:  0.0009477229999959036\n",
      "time2:  0.0009352520000049935\n",
      "time3:  0.0016761059999907957\n",
      "Gaussian_samples_KL_div1:  14.264435669275697\n",
      "Gaussian_samples_KL_div2:  10.52531475596854\n",
      "Gaussian_samples_KL_div3:  8.15437240100636\n",
      "time1:  0.0011616120000041974\n",
      "time2:  0.001142592999997305\n",
      "time3:  0.0012315259999979844\n",
      "Gaussian_samples_KL_div1:  5.965778600535028\n",
      "Gaussian_samples_KL_div2:  6.198019970594516\n",
      "Gaussian_samples_KL_div3:  4.114394381548063\n",
      "time1:  0.002395892999999205\n",
      "time2:  0.0025036650000060945\n",
      "time3:  0.0023939959999950133\n",
      "Gaussian_samples_KL_div1:  2.397511389750594\n",
      "Gaussian_samples_KL_div2:  3.626993547955287\n",
      "Gaussian_samples_KL_div3:  0.7100068140616561\n",
      "time1:  0.005437107000005881\n",
      "time2:  0.004401690999998209\n",
      "time3:  0.004326246000005085\n",
      "Gaussian_samples_KL_div1:  2.1040250681833075\n",
      "Gaussian_samples_KL_div2:  2.560801119391448\n",
      "Gaussian_samples_KL_div3:  0.7781830507510847\n",
      "time1:  0.006406613999985211\n",
      "time2:  0.0063892739999857895\n",
      "time3:  0.006320517000006021\n",
      "Gaussian_samples_KL_div1:  1.1129971030305017\n",
      "Gaussian_samples_KL_div2:  2.160143594996754\n",
      "Gaussian_samples_KL_div3:  0.38091637279086044\n",
      "time1:  0.008419486000008192\n",
      "time2:  0.008469096999988324\n",
      "time3:  0.00856136999999535\n",
      "Gaussian_samples_KL_div1:  0.3335837338042414\n",
      "Gaussian_samples_KL_div2:  1.1205779169442525\n",
      "Gaussian_samples_KL_div3:  0.20704649619321633\n",
      "time1:  0.020737985000010895\n",
      "time2:  0.02081458800000746\n",
      "time3:  0.021008805000008124\n",
      "Gaussian_samples_KL_div1:  0.22522943940085424\n",
      "Gaussian_samples_KL_div2:  0.5825294030800909\n",
      "Gaussian_samples_KL_div3:  0.16253018498816432\n",
      "time1:  0.04184409699999492\n",
      "time2:  0.041405582999999524\n",
      "time3:  0.04310737700001255\n",
      "Gaussian_samples_KL_div1:  0.13489024581679096\n",
      "Gaussian_samples_KL_div2:  0.3488207641013853\n",
      "Gaussian_samples_KL_div3:  0.04597896609399346\n",
      "time1:  0.12406357200001139\n",
      "time2:  0.12427315899998348\n",
      "time3:  0.12361004800001751\n",
      "Gaussian_samples_KL_div1:  0.09172126367967334\n",
      "Gaussian_samples_KL_div2:  0.25185713600015136\n",
      "Gaussian_samples_KL_div3:  0.041651984986226596\n",
      "time1:  0.16506682599998612\n",
      "time2:  0.1654048839999973\n",
      "time3:  0.170697290999982\n",
      "Gaussian_samples_KL_div1:  0.04460225984044611\n",
      "Gaussian_samples_KL_div2:  0.09400384277066848\n",
      "Gaussian_samples_KL_div3:  0.022745525735881032\n",
      "time1:  0.4152961140000002\n",
      "time2:  0.40570551199999727\n",
      "time3:  0.4111220839999987\n",
      "Gaussian_samples_KL_div1:  0.016448324662002356\n",
      "Gaussian_samples_KL_div2:  0.03634872540745392\n",
      "Gaussian_samples_KL_div3:  0.008888164439510049\n",
      "time1:  0.6218831209999962\n",
      "time2:  0.6146956320000072\n",
      "time3:  0.6155014460000245\n",
      "Gaussian_samples_KL_div1:  0.012018209478634372\n",
      "Gaussian_samples_KL_div2:  0.02479119750394382\n",
      "Gaussian_samples_KL_div3:  0.008333545553341431\n",
      "time1:  0.8355310869999926\n",
      "time2:  0.8291337189999979\n",
      "time3:  0.8312882089999789\n",
      "Gaussian_samples_KL_div1:  0.012716298975076154\n",
      "Gaussian_samples_KL_div2:  0.016087317918594007\n",
      "Gaussian_samples_KL_div3:  0.005783522474822774\n",
      "time1:  1.0443956050000054\n",
      "time2:  1.034801664000014\n",
      "time3:  1.03371510300002\n",
      "[array([4.13722703e+01, 3.89436245e+01, 3.65396295e+01, 2.80231175e+01,\n",
      "       2.21930920e+01, 1.74325753e+01, 1.13890840e+01, 6.06096435e+00,\n",
      "       3.12026773e+00, 1.99973241e+00, 1.29681742e+00, 4.62013990e-01,\n",
      "       2.66474886e-01, 1.44260695e-01, 8.62612075e-02, 4.09931077e-02,\n",
      "       1.88979392e-02, 1.49466546e-02, 1.11071108e-02]), array([4.13722703e+01, 3.90969503e+01, 3.69867455e+01, 3.03161187e+01,\n",
      "       2.48824334e+01, 1.62143203e+01, 1.51328999e+01, 6.10507730e+00,\n",
      "       3.73052344e+00, 1.98997644e+00, 1.17011009e+00, 4.21208242e-01,\n",
      "       2.29324842e-01, 1.49632844e-01, 8.53734147e-02, 3.62951556e-02,\n",
      "       2.46432531e-02, 1.31507032e-02, 1.05391900e-02]), array([4.13722703e+01, 3.89702898e+01, 3.65930034e+01, 3.13282135e+01,\n",
      "       2.32525842e+01, 1.75764546e+01, 1.34855687e+01, 5.43192287e+00,\n",
      "       2.37952838e+00, 1.68092069e+00, 1.06936165e+00, 5.32809587e-01,\n",
      "       2.67596314e-01, 1.68185075e-01, 1.15763559e-01, 3.85089638e-02,\n",
      "       2.15901477e-02, 1.94219384e-02, 1.25384250e-02]), array([4.13722703e+01, 3.87316396e+01, 3.46470427e+01, 3.14535128e+01,\n",
      "       2.28333732e+01, 1.76011730e+01, 1.51900902e+01, 6.40062828e+00,\n",
      "       2.41278649e+00, 1.41835539e+00, 1.23598736e+00, 4.26525045e-01,\n",
      "       2.87423322e-01, 1.64804371e-01, 9.82654587e-02, 3.55331650e-02,\n",
      "       2.13479805e-02, 1.35894913e-02, 9.38493658e-03]), array([4.13722703e+01, 3.89636235e+01, 3.57346457e+01, 3.07678861e+01,\n",
      "       2.04988414e+01, 1.69827728e+01, 1.42644357e+01, 5.96577860e+00,\n",
      "       2.39751139e+00, 2.10402507e+00, 1.11299710e+00, 3.33583734e-01,\n",
      "       2.25229439e-01, 1.34890246e-01, 9.17212637e-02, 4.46022598e-02,\n",
      "       1.64483247e-02, 1.20182095e-02, 1.27162990e-02])]\n"
     ]
    }
   ],
   "source": [
    "seeds = [123, 234, 345, 456, 567]\n",
    "KL1_Gaussian_mean, KL2_Gaussian_mean, KL3_Gaussian_mean, KL1_Gaussian_std, KL2_Gaussian_std, KL3_Gaussian_std, \\\n",
    "KL1_Dirichlet, KL2_Dirichlet,  KL3_Dirichlet, Gaussian1_timing_mean, Gaussian2_timing_mean,\\\n",
    "Gaussian3_timing_mean, Gaussian1_timing_std, Gaussian2_timing_std, Gaussian3_timing_std = Gaussian_vs_Dirichlet(seeds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.13722703e+01 3.89412255e+01 3.61002133e+01 3.03777697e+01\n",
      " 2.27320648e+01 1.71614592e+01 1.38924157e+01 5.99287428e+00\n",
      " 2.80812349e+00 1.83860200e+00 1.17705473e+00 4.35228119e-01\n",
      " 2.55209761e-01 1.52354646e-01 9.54769807e-02 3.91865304e-02\n",
      " 2.05855290e-02 1.46253994e-02 1.12571923e-02] 0.08817099700242213\n"
     ]
    }
   ],
   "source": [
    "# calculate the cutoff points\n",
    "print(KL1_Gaussian_mean,  KL1_Dirichlet)\n",
    "sample_sizes = [1, 5,   10, 25, 50, 75,\n",
    "                        100, 250, 500, 750,\n",
    "                        1000, 2500, 5000, 7500,\n",
    "                        10000, 25000, 50000, 75000,\n",
    "                        100000]\n",
    "cutoff1 = sample_sizes[np.sum(KL1_Gaussian_mean>KL1_Dirichlet)]\n",
    "cutoff2 = sample_sizes[np.sum(KL2_Gaussian_mean>KL2_Dirichlet)]\n",
    "cutoff3 = sample_sizes[np.sum(KL3_Gaussian_mean>KL3_Dirichlet)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tikzplotlib as tpl\n",
    "from matplotlib.patches import Patch\n",
    "from matplotlib.lines import Line2D\n",
    "#### sample_sizes ####\n",
    "fig = plt.figure()\n",
    "\n",
    "plt.rcParams['xtick.labelsize'] = 25\n",
    "plt.rcParams['ytick.labelsize'] = 25\n",
    "plt.rcParams[\"figure.figsize\"] = (10,5)\n",
    "plt.rcParams[\"font.family\"] = \"serif\"\n",
    "plt.rcParams[\"font.serif\"] = \"Times New Roman\"\n",
    "\n",
    "n = len(sample_sizes)\n",
    "sample_line1 = [1, cutoff1]\n",
    "sample_line2 = [1, cutoff2]\n",
    "sample_line3 = [1, cutoff3]\n",
    "#plt.rcParams[\"figure.figsize\"] = (20,8)\n",
    "plt.errorbar(sample_sizes, KL1_Gaussian_mean, yerr=KL1_Gaussian_std, lw=3, color=\"blue\", label='Monte Carlo')\n",
    "plt.errorbar(sample_sizes, KL2_Gaussian_mean, yerr=KL2_Gaussian_std, lw=3, color=\"orange\")#, label='KL2 Gaussian')\n",
    "plt.errorbar(sample_sizes, KL3_Gaussian_mean, yerr=KL3_Gaussian_std, lw=3, color=\"green\")#, label='KL3 Gaussian')\n",
    "plt.plot(1, KL1_Dirichlet, 'o', color=\"red\", label = 'Laplace Bridge')\n",
    "plt.plot(1, KL2_Dirichlet, 'o', color=\"purple\")#, label = 'KL2 Dirichlet')\n",
    "plt.plot(1, KL3_Dirichlet, 'o', color=\"brown\")#, label = 'KL3 Dirichlet')\n",
    "plt.plot(sample_line1, [KL1_Dirichlet]*2, '-.', lw=3, alpha=0.5, color=\"red\")\n",
    "plt.plot(sample_line2, [KL2_Dirichlet]*2, '-.', lw=3, alpha=0.5, color=\"purple\")\n",
    "plt.plot(sample_line3, [KL3_Dirichlet]*2, '-.', lw=3, alpha=0.5, color=\"brown\")\n",
    "#cutoff points\n",
    "plt.vlines(cutoff1, ymin=0, ymax=7, alpha=0.7, color=\"blue\")#, label='equal KL div 1')\n",
    "plt.vlines(cutoff2, ymin=0, ymax=7, alpha=0.7, color=\"orange\")#, label='equal KL div 2')\n",
    "plt.vlines(cutoff3, ymin=0, ymax=7, alpha=0.7, color=\"green\")#, label='equal KL div 3')\n",
    "plt.ylabel('KL Divergence', fontdict={'fontsize':25})\n",
    "plt.xlabel('Number of Samples', fontdict={'fontsize':25})\n",
    "plt.xscale('log');\n",
    "plt.legend(loc='upper right', prop={'size': 25})\n",
    "#plt.savefig('figures/KL_div_playground_samples.pdf')\n",
    "plt.tick_params(which='both',\n",
    "                top=False,\n",
    "                right=False,\n",
    "                direction='in')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.savefig('figures/KLDivSamples.pdf')\n",
    "\n",
    "plt.show()\n",
    "#tpl.save('figures/KLDivSamples.tex', figure=fig, figurewidth='\\\\figwidth', figureheight='\\\\figheight',\n",
    "#        extra_axis_parameters={'xtick align=inside', 'ytick align=inside', 'xtick pos=left', 'ytick pos=left', 'legend pos=north east'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate the cutoff points\n",
    "cutoff1_time = Gaussian1_timing_mean[np.sum(KL1_Gaussian_mean>KL1_Dirichlet)]\n",
    "cutoff2_time = Gaussian2_timing_mean[np.sum(KL2_Gaussian_mean>KL2_Dirichlet)]\n",
    "cutoff3_time = Gaussian3_timing_mean[np.sum(KL3_Gaussian_mean>KL3_Dirichlet)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "##### timing ####\n",
    "fig = plt.figure()\n",
    "\n",
    "plt.rcParams['xtick.labelsize'] = 25\n",
    "plt.rcParams['ytick.labelsize'] = 25\n",
    "plt.rcParams[\"font.family\"] = \"serif\"\n",
    "plt.rcParams[\"font.serif\"] = \"Times New Roman\"\n",
    "plt.rcParams[\"figure.figsize\"] = (10,5)\n",
    "\n",
    "n = len(sample_sizes)\n",
    "time_line1 = [Dirichlet_1_time, cutoff1_time]\n",
    "time_line2 = [Dirichlet_2_time, cutoff2_time]\n",
    "time_line3 = [Dirichlet_3_time, cutoff3_time]\n",
    "#plt.rcParams[\"figure.figsize\"] = (20,8)\n",
    "plt.errorbar(Gaussian1_timing_mean, KL1_Gaussian_mean, yerr=KL1_Gaussian_std, lw=3, color=\"blue\", label='Monte Carlo')\n",
    "plt.errorbar(Gaussian2_timing_mean, KL2_Gaussian_mean, yerr=KL2_Gaussian_std, lw=3, color=\"orange\")#, label='KL2 Gaussian')\n",
    "plt.errorbar(Gaussian3_timing_mean, KL3_Gaussian_mean, yerr=KL3_Gaussian_std, lw=3, color=\"green\")#, label='KL3 Gaussian')\n",
    "plt.plot(Dirichlet_1_time, KL1_Dirichlet, 'o', color=\"red\", label = 'Laplace Bridge')\n",
    "plt.plot(Dirichlet_2_time, KL2_Dirichlet, 'o', color=\"purple\")#, label = 'KL2 Dirichlet')\n",
    "plt.plot(Dirichlet_3_time, KL3_Dirichlet, 'o', color=\"brown\")#, label = 'KL3 Dirichlet')\n",
    "plt.plot(time_line1, [KL1_Dirichlet]*2, '-.', lw=3, alpha=0.5, color=\"red\")\n",
    "plt.plot(time_line2, [KL2_Dirichlet]*2, '-.', lw=3, alpha=0.5, color=\"purple\")\n",
    "plt.plot(time_line3, [KL3_Dirichlet]*2, '-.', lw=3, alpha=0.5, color=\"brown\")\n",
    "#cutoff points\n",
    "plt.vlines(cutoff1_time, ymin=0, ymax=7, alpha=0.7, color=\"blue\")#, label='equal KL div 1')\n",
    "plt.vlines(cutoff2_time, ymin=0, ymax=7, alpha=0.7, color=\"orange\")#, label='equal KL div 2')\n",
    "plt.vlines(cutoff3_time, ymin=0, ymax=7, alpha=0.7, color=\"green\")#, label='equal KL div 3')\n",
    "plt.ylabel('KL Divergence', fontdict={'fontsize':25})\n",
    "plt.xlabel('Time in s', fontdict={'fontsize':25})\n",
    "plt.xscale('log');\n",
    "\n",
    "leg = plt.legend(loc='upper right', prop={'size': 25})\n",
    "plt.tick_params(which='both',\n",
    "                top=False,\n",
    "                right=False,\n",
    "                direction='in')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.savefig('figures/KLDivTime.pdf')\n",
    "\n",
    "plt.show()\n",
    "#tpl.save('figures/KLDivTime.tex', figure=fig, figurewidth='\\\\figwidth', figureheight='\\\\figheight',\n",
    "#         extra_axis_parameters={'xtick align=inside', 'ytick align=inside', 'xtick pos=left', 'ytick pos=left', 'legend pos=north east'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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